liu.seSearch for publications in DiVA
Change search
Refine search result
12 1 - 50 of 72
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the 'Create feeds' function.
  • 1.
    Adamowicz, Tomasz
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points2014In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 31, no 6, p. 1131-1153Article in journal (Refereed)
    Abstract [en]

    We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for p(.)-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded p(.)-harmonic functions and give some new characterizations of W-0(1,p(.)) spaces. We also show that p(.)-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.

  • 2.
    Adamowicz, Tomasz
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Shanmugalingam, Nageswari
    University of Cincinnati, OH USA .
    Prime ends for domains in metric spaces2013In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 238, p. 459-505Article in journal (Refereed)
    Abstract [en]

    In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Caratheodory and Nakki. Modulus ends and prime ends, defined by means of the p-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.

  • 3.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces2016In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 134, p. 70-104Article in journal (Refereed)
    Abstract [en]

    We develop a framework for studying variational problems in Banach spaces with respect to gradient relations, which encompasses many of the notions of generalized gradients that appear in the literature. We stress the fact that our approach is not dependent on function spaces and therefore applies equally well to functions on metric spaces as to operator algebras. In particular, we consider analogues of Dirichlet and obstacle problems, as well as first eigenvalue problems, and formulate conditions for the existence of solutions and their uniqueness. Moreover, we investigate to what extent a lattice structure may be introduced on ( ordered) Banach spaces via a norm-minimizing variational problem. A multitude of examples is provided to illustrate the versatility of our approach. (C) 2015 Elsevier Ltd. All rights reserved.

  • 4.
    Björn , Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations2009In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, ISSN 0944-2669 , Vol. 35, no 4, p. 481-496Article in journal (Refereed)
    Abstract [en]

    We use variational methods to obtain a pointwise estimate near a boundary point for quasisubminimizers of the p-energy integral and other integral functionals in doubling metric measure spaces admitting a p-Poincar, inequality. It implies a Wiener type condition necessary for boundary regularity for p-harmonic functions on metric spaces, as well as for (quasi)minimizers of various integral functionals and solutions of nonlinear elliptic equations on R (n) .

  • 5.
    Björn, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Approximations by regular sets and Wiener solutions in metric spaces2007In: Commentationes mathematicae Universitatis Carolinae, ISSN 0323-0171, Vol. 48, no 2, p. 343-355Article in journal (Refereed)
  • 6.
    Björn, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces2004Report (Other academic)
  • 7.
    Björn, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces2006In: Journal of the Mathematical Society of Japan, ISSN 0025-5645, E-ISSN 1881-1167, Vol. 58, no 4, p. 1211-1232Article in journal (Refereed)
    Abstract [en]

    We study p-harmonic functions in complete metric spaces equipped with a doubling Borel measure supporting a weak (1, p)-Poincaré inequality, 1 < p < ∞. We establish the barrier classification of regular boundary points from which it also follows that regularity is a local property of the boundary. We also prove boundary regularity at the fixed (given) boundary for solutions of the one-sided obstacle problem on bounded open sets. Regularity is further characterized in several other ways. Our results apply also to Cheeger p-harmonic functions and in the Euclidean setting to script A sign-harmonic functions, with the usual assumptions on script A sign.

  • 8.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    First-order Sobolev spaces on metric spaces2009In: Function Spaces, Inequalities and Interpolation (Paseky, 2009) / [ed] Jaroslav Lukes, Lubos Pick, Prague: Matfyzpress , 2009, p. 1-29Conference paper (Refereed)
  • 9.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Nonlinear Potential Theory on Metric Spaces2011 (ed. 1)Book (Refereed)
    Abstract [en]

    The p-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories.

    This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for an interested reader and as a reference text for an active researcher. The presentation is rather self-contained, but the reader is assumed to know measure theory and functional analysis.

    The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space.

    Each chapter contains historical notes with relevant references and an extensive index is provided at the end of the book.

  • 10.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology2015In: Revista matemática iberoamericana, ISSN 0213-2230, E-ISSN 2235-0616, Vol. 31, no 1, p. 161-214Article in journal (Refereed)
    Abstract [en]

    We study the double obstacle problem for p-harmonic functions on arbitrary bounded nonopen sets E in quite general metric spaces. The Dirichlet and single obstacle problems are included as special cases. We obtain the Adams criterion for the solubility of the single obstacle problem and establish connections with fine potential theory. We also study when the minimal p-weak upper gradient of a function remains minimal when restricted to a nonopen subset. Many of the results are new even for open E (apart from those which are trivial in this case) and also on R-n.

  • 11.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    POWER-TYPE QUASIMINIMIZERS2011In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, ISSN 1239-629X, Vol. 36, no 1, p. 301-319Article in journal (Refereed)
    Abstract [en]

    In this paper we examine the quasiminimizing properties of radial power-type functions u(x) = vertical bar x vertical bar(alpha) in R-n. We find the optimal quasiminimizing constant whenever u is a quasiminfinizer of the p-Dirichlet integral, p not equal n, and similar results when u is a quasisub- and quasisuperminimizer. We also obtain similar results for log-powers when p = n.

  • 12.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    The Variational Capacity with Respect to Nonopen Sets in Metric Spaces2014In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 40, no 1, p. 57-80Article in journal (Refereed)
    Abstract [en]

    We pursue a systematic treatment of the variational capacity on metric spaces and give full proofs of its basic properties. A novelty is that we study it with respect to nonopen sets, which is important for Dirichlet and obstacle problems on nonopen sets, with applications in fine potential theory. Under standard assumptions on the underlying metric space, we show that the variational capacity is a Choquet capacity and we provide several equivalent definitions for it. On open sets in weighted R (n) it is shown to coincide with the usual variational capacity considered in the literature. Since some desirable properties fail on general nonopen sets, we introduce a related capacity which turns out to be a Choquet capacity in general metric spaces and for many sets coincides with the variational capacity. We provide examples demonstrating various properties of both capacities and counterexamples for when they fail. Finally, we discuss how a change of the underlying metric space influences the variational capacity and its minimizing functions.

  • 13.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Gianazza, Ugo
    University of Pavia, Italy.
    The Petrovskii criterion and barriers for degenerate and singular p-parabolic equations2017In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 368, no 3-4, p. 885-904Article in journal (Refereed)
    Abstract [en]

    In this paper we obtain sharp Petrovskii criteria for the p-parabolic equation, both in the degenerate case p amp;gt; 2 and the singular case 1 amp;lt; p amp;lt; 2 We also give an example of an irregular boundary point at which there is a barrier, thus showing that regularity cannot be characterized by the existence of just one barrier.

  • 14.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Gianazza, Ugo
    University of Pavia, Italy.
    Parviainen, Mikko
    University of Jyvaskyla, Finland.
    Boundary regularity for degenerate and singular parabolic equations2015In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 52, no 3-4, p. 797-827Article in journal (Refereed)
    Abstract [en]

    We characterise regular boundary points of the parabolic p-Laplacian in terms of a family of barriers, both when p greater than 2 and 1 less than p less than 2. By constructing suitable families of such barriers, we give some simple geometric conditions that ensure the regularity of boundary points.

  • 15.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Gill, James T.
    St Louis University, MO 63103 USA.
    Shanmugalingam, Nageswari
    University of Cincinnati, OH 45221 USA.
    Geometric analysis on Cantor sets and trees2017In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 725, p. 63-114Article in journal (Refereed)
    Abstract [en]

    dUsing uniformization, Cantor type sets can be regarded as boundaries of rooted trees. In this setting, we show that the trace of a first-order Sobolev space on the boundary of a regular rooted tree is exactly a Besov space with an explicit smoothness exponent. Further, we study quasisymmetries between the boundaries of two trees, and show that they have rough quasiisometric extensions to the trees. Conversely, we show that every rough quasiisometry between two trees extends as a quasisymmetry between their boundaries. In both directions we give sharp estimates for the involved constants. We use this to obtain quasisymmetric invariance of certain Besov spaces of functions on Cantor type sets.

  • 16.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Korte, Riikka
    Aalto University, Finland.
    Minima of quasisuperminimizers2017In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 155, p. 264-284Article in journal (Refereed)
    Abstract [en]

    We show that, unlike minima of superharmonic functions which are again superharmonic, the same property fails for Q-quasisuperminimizers. More precisely, if u(i) is a Q(i)-quasisuperminimizer, i = 1,2, where 1 amp;lt; Q(1) amp;lt; Q(2), then u = min{u(1), u(2)} is a Q-quasisuperminimizer, but there is an increase in the optimal quasisuperminimizing constant Q. We provide the first examples of this phenomenon, i.e. that Q amp;gt; Q(2). In addition to lower bounds for the optimal quasisuperminimizing constant of u we also improve upon the earlier upper bounds due to Kinnunen and Martio. Moreover, our lower and upper bounds turn out to be quite close. We also study a similar phenomenon in pasting lemmas for quasisuperminimizers, where Q = Q(1)Q(2) turns out to be optimal, and provide results on exact quasiminimizing constants of piecewise linear functions on the real line, which can serve as approximations of more general quasiminimizers. (C) 2017 Elsevier Ltd. All rights reserved.

  • 17.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Latvala, Visa
    University of Eastern Finland, Finland.
    SOBOLEV SPACES, FINE GRADIENTS AND QUASICONTINUITY ON QUASIOPEN SETS2016In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 41, no 2, p. 551-560Article in journal (Refereed)
    Abstract [en]

    We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space X equipped with a doubling measure supporting a p-Poincare inequality with 1 amp;lt; p amp;lt; infinity, and connect them to the Sobolev theory in R-n. In particular, we show that for quasiopen subsets of R-n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpelainen and Maly in 1992.

  • 18.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Latvala, Visa
    University of Eastern Finland, Finland.
    The Weak Cartan Property for the p-fine Topology on Metric Spaces2015In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 64, no 3, p. 915-941Article in journal (Refereed)
    Abstract [en]

    We study the p-fine topology on complete metric spaces equipped with a doubling measure supporting a p-Poincare inequality, 1 less than p less than infinity. We establish a weak Cartan property, which yields characterizations of the p-thinness and the p-fine continuity, and allows us to show that the p-fine topology is the coarsest topology making all p-superharmonic functions continuous. Our p-harmonic and superharmonic functions are defined by means of scalar-valued upper gradients, and do not rely on a vector-valued differentiable structure.

  • 19.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Lehrback, Juha
    University of Jyvaskyla, Finland.
    Sharp capacity estimates for annuli in weighted R-n and in metric spaces2017In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 286, no 3-4, p. 1173-1215Article in journal (Refereed)
    Abstract [en]

    We obtain estimates for the nonlinear variational capacity of annuli in weighted R-n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R-n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R-n, which are based on quasiconformality of radial stretchings in R-n.

  • 20.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Lehrback, Juha
    University of Jyväskylä, Finland.
    The annular decay property and capacity estimates for thin annuli2017In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 68, no 2, p. 229-241Article in journal (Refereed)
    Abstract [en]

    We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted and in metric spaces, primarily under the assumptions of an annular decay property and a Poincar, inequality. In particular, if the measure has the 1-annular decay property at and the metric space supports a pointwise 1-Poincar, inequality at , then the upper and lower bounds are comparable and we get a two-sided estimate for thin annuli centred at . This generalizes the known estimate for the usual variational capacity in unweighted . We also characterize the 1-annular decay property and provide examples which illustrate the sharpness of our results.

  • 21.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Maly, Jan
    University of JE Purkyne, Czech Republic.
    Quasiopen and p-Path Open Sets, and Characterizations of Quasicontinuity2017In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 46, no 1, p. 181-199Article in journal (Refereed)
    Abstract [en]

    In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincar, inequality we show that quasiopen and p-path open sets coincide. Under the same assumptions we show that all Newton-Sobolev functions on quasiopen sets are quasicontinuous.

  • 22.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Marola, Niko
    University of Helsinki.
    BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers2010In: ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, ISSN 0294-1449, Vol. 27, no 6, p. 1489-1505Article in journal (Refereed)
    Abstract [en]

    In this paper we use quasiminimizing properties of radial power-type functions to deduce counterexamples to certain Caccioppoli type inequalities and weak Harnack inequalities for quasisuperharmonic functions both of which are well known to hold for p-superharmonic functions We also obtain new bounds on the local integrability for quasisuperharmonic functions Furthermore we show that the logarithm of a positive quasisuperminimizer has bounded mean oscillation and belongs to a Sobolev type space

  • 23.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mäkäläinen, Tero
    University of Jyväskylä.
    Parviainen, Mikko
    Helsinki University of Technology.
    Nonlinear balayage on metric spaces2009In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, no 5-6, p. 2153-2171Article in journal (Refereed)
    Abstract [en]

    We develop a theory of balayage on complete doubling metric measure spaces supporting a Poincaré inequality. In particular, we are interested in continuity and p-harmonicity of the balayage. We also study connections to the obstacle problem. As applications, we characterize regular boundary points and polar sets in terms of balayage.

  • 24.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Parviainen, Mikko
    Helsinki University of Technology.
    Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces2008Report (Other academic)
  • 25.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Parviainen, Mikko
    Helsinki University Technology.
    Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces2010In: REVISTA MATEMATICA IBEROAMERICANA, ISSN 0213-2230, Vol. 26, no 1, p. 147-174Article in journal (Refereed)
    Abstract [en]

    We prove the nonlinear fundamental convergence theorem for superharmonic functions on metric measure spaces. Our proof seems to be new even in the Euclidean setting. The proof uses direct methods in the calculus of variations and, in particular, avoids advanced tools from potential theory. We also provide a new proof for the fact that a Newtonian function has Lebesgue points outside a set of capacity zero, and give a sharp result on when superharmonic functions have L-q-Lebesgue points everywhere.

  • 26.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Shanmugalingam , Nageswari
    University of Cincinnati.
    A problem of Baernstein on the equality of the p-harmonic measure of a set and its closure2006In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 134, no 3, p. 509-519Article in journal (Refereed)
    Abstract [en]

    A. Baernstein II (Comparison of p-harmonic measures of subsets of the unit circle, St. Petersburg Math. J. 9 (1998), 543-551, p. 548), posed the following question: If G is a union of m open arcs on the boundary of the unit disc D, then is w a,p(G)=w a,p(G), where w a,p denotes the p-harmonic measure? (Strictly speaking he stated this question for the case m=2.) For p=2 the positive answer to this question is well known. Recall that for p≠2 the p-harmonic measure, being a nonlinear analogue of the harmonic measure, is not a measure in the usual sense.

    The purpose of this note is to answer a more general version of Baernstein's question in the affirmative when 1G is the restriction to ∂D of a Sobolev function from W 1,p(C).

    For p≥2 it is no longer true that XG belongs to the trace class. Nevertheless, we are able to show equality for the case m=1 of one arc for all 1, using a very elementary argument. A similar argument is used to obtain a result for starshaped domains.

    Finally we show that in a certain sense the equality holds for almost all relatively open sets.

  • 27.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Shanmugalingam , Nageswari
    University of Cincinnati.
    Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions on metric spaces2008In: Houston Journal of Mathematics, ISSN 0362-1588, Vol. 34, no 4, p. 1197-1211Article in journal (Refereed)
    Abstract [en]

    We show that on complete doubling metric measure spaces X supporting a Poincare inequality, all Newton-Sobolev functions u are quasicontinuous, i.e. that for every epsilon > 0 there is an open set U subset of X such that C-p(U) < epsilon and the restriction of u to X\U is continuous. This implies that the capacity is an outer capacity.

  • 28.
    Björn, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shanmugalingam, Nageswari
    A problem of Baernstein on the equality of the p-harmonic measure of a set and its closure2003Report (Other academic)
  • 29.
    Björn, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shanmugalingam, Nageswari
    Sobolev extensions of Hölder continuous and characteristic functions on metric spaces2005Report (Other academic)
  • 30.
    Björn, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shanmugalingam, Nageswari
    Department of Mathematical Sciences University of Cincinnati.
    Sobolev extensions of Hölder continuous and characteristic functions on metric spaces2007In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-2479, Vol. 59, no 6, p. 1135-1153Article in journal (Refereed)
    Abstract [en]

    We study when characteristic and Holder continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and Hölder continuous functions into globally defined Sobolev functions. ©Canadian Mathematical Society 2007.

  • 31.
    Björn, Anders
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Shanmugalingam, Nageswari
    The Dirichlet problem for p-harmonic functions on metric spaces2003In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, no 556, p. 173-203Article in journal (Refereed)
    Abstract [en]

    We study the Dirichlet problem for p-harmonic functions (and p-energy minimizers) in bounded domains in proper, pathconnected metric measure spaces equipped with a doubling measure and supporting a PoincarΘ inequality. The Dirichlet problem has previously been solved for Sobolev type boundary data, and we extend this result and solve the problem for all continuous boundary data. We study the regularity of boundary points and prove the Kellogg property, i.e. that the set of irregular boundary points has zero p-capacity. We also construct p-capacitary, p-singular and p-harmonic measures on the boundary. We show that they are all absolutely continuous with respect to the p-capacity. For p = 2 we show that all the boundary measures are comparable and that the singular and harmonic measures coincide. We give an integral representation for the solution to the Dirichlet problem when p = 2, enabling us to extend the solvability of the problem to L1 boundary data in this case. Moreover, we give a trace result for Newtonian functions when p = 2. Finally, we give an estimate for the Hausdorff dimension of the boundary of a bounded domain in Ahlfors Q-regular spaces.

  • 32.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Shanmugalingam, Nageswari
    University of Cincinnati, OH 45221 USA.
    The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities2015In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 7, p. 3078-3114Article in journal (Refereed)
    Abstract [en]

    In this paper we develop the Perron method for solving the Dirichlet problem for the analog of the p-Laplacian, i.e. for p-harmonic functions, with Mazurkiewicz boundary values. The setting considered here is that of metric spaces, where the boundary of the domain in question is replaced with the Mazurkiewicz boundary. Resolutivity for Sobolev and continuous functions, as well as invariance results for perturbations on small sets, are obtained. We use these results to improve the known resolutivity and invariance results for functions on the standard (metric) boundary. We also illustrate the results of this paper by discussing several examples. (C) 2015 Elsevier Inc. All rights reserved.

  • 33.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Shanmugalingam, Nageswari
    University of Cincinnati, OH 45221 USA.
    The Mazurkiewicz Distance and Sets that are Finitely Connected at the Boundary2016In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 26, no 2, p. 873-897Article in journal (Refereed)
    Abstract [en]

    We study local connectedness, local accessibility and finite connectedness at the boundary, in relation to the compactness of the Mazurkiewicz completion of a bounded domain in a metric space. For countably connected planar domains we obtain a complete characterization. It is also shown exactly which parts of this characterization fail in higher dimensions and in metric spaces.

  • 34.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Shanmugalingam, Nageswari
    University of Cincinnati.
    The Perron method for p-harmonic functions in metric spaces2003In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 195, no 2, p. 398-429Article in journal (Refereed)
    Abstract [en]

    We use the Perron method to construct and study solutions of the Dirichlet problem for p-harmonic functions in proper metric measure spaces endowed with a doubling Borel measure supporting a weak (1,q)-Poincaré inequality (for some 1q<p). The upper and lower Perron solutions are constructed for functions defined on the boundary of a bounded domain and it is shown that these solutions are p-harmonic in the domain. It is also shown that Newtonian (Sobolev) functions and continuous functions are resolutive, i.e. that their upper and lower Perron solutions coincide, and that their Perron solutions are invariant under perturbations of the function on a set of capacity zero. We further study the problem of resolutivity and invariance under perturbations for semicontinuous functions. We also characterize removable sets for bounded p-(super)harmonic functions.

  • 35.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Approximations by regular sets in metric spaces2004Report (Other academic)
  • 36.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Boundary regularity for p-harmonic functions on metric spaces2004In: International Workshop on Potential Theory in Matsue 2004,2004, 2004Conference paper (Other academic)
    Abstract [en]

       

  • 37.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Boundary regularity for p-harmonic functions on metric spaces2004In: Analysis on Metric Measure Spaces,2004, 2004Conference paper (Other academic)
    Abstract [en]

      

  • 38.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Boundary regularity for p-harmonic functions on metric spaces2004In: The p-Laplace equation, the infinity-Laplace equation and related topics,2004, 2004Conference paper (Other academic)
    Abstract [en]

      

  • 39.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Boundary regularity for quasiminimizers2015Conference paper (Other academic)
    Abstract [en]

  • 40.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Boundary regularity for quasiminimizers2015Conference paper (Other academic)
    Abstract [en]

  • 41.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    De Giorgi's method: in(s) and out(s)2011Conference paper (Refereed)
    Abstract [en]

    One of the main break-throughs in the 20th century mathematics was De Giorgi's proof of Hölder continuity for solutions of elliptic PDEs. His method has since then been used to prove interior regularity in various contexts.It is maybe less known, though not entirely surprising that De Giorgi's method also yields sufficient conditions for boundary regularity. In the talk, I will discuss a recent variation of De Giorgi's method which goes in the opposite direction, leading to a necessary condition for boundary regularity of PDEs and variational integrals.

  • 42.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Dirichlet problem for $p$-harmonic functions in metric spaces2003In: Future Trends in Geometric Function Theory RNC Workshop Jyväskylä 2003,2003, Jyväskylä: University of Jyväskylä, Department of Mathematics and Statistics , 2003, p. 31-Conference paper (Refereed)
  • 43.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Dirichlet problem on bad sets and fine topology2011Conference paper (Refereed)
  • 44.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Fine continuity on metric spaces2007Report (Other academic)
  • 45.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Fine continuity on metric spaces2008In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 125, no 3, p. 369-381Article in journal (Refereed)
    Abstract [en]

    We obtain pointwise estimates for solutions of obstacle problems on metric measure spaces and prove that p-superharmonic functions are p-finely continuous. Consequently, we show that p-quasicontinuous functions are p-finely continuous at p-quasievery point. As a byproduct, we obtain the sufficiency part of the Wiener criterion in metric spaces without the assumption of linear local connectedness. © 2007 Springer-Verlag.

  • 46.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Fine topology by means of potential theory on metric spaces2013Conference paper (Refereed)
  • 47.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Fine topology by means of potential theory on metric spaces2013Conference paper (Refereed)
  • 48.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    L-q-differentials for weighted Sobolev spaces2000In: The Michigan mathematical journal, ISSN 0026-2285, E-ISSN 1945-2365, Vol. 47, no 1, p. 151-161Article in journal (Refereed)
  • 49.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Metrics, prime ends and the Dirichlet problem on bad domains2013Conference paper (Refereed)
  • 50.
    Björn, Jana
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Necessity of a Wiener type condition for boundary regularity on metric spaces2007Report (Other academic)
    Abstract [en]

      

12 1 - 50 of 72
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf