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Björn, A., Björn, J. & Latvala, V. (2023). Correction: The Dirichlet Problem for p-minimizers on Finely Open Sets in Metric Spaces (May, 10.1007/s11118-022-09996-7, 2022). Potential Analysis, 59, 2131-2132
Open this publication in new window or tab >>Correction: The Dirichlet Problem for p-minimizers on Finely Open Sets in Metric Spaces (May, 10.1007/s11118-022-09996-7, 2022)
2023 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 59, p. 2131-2132Article in journal (Other academic) Published
Place, publisher, year, edition, pages
Dordrecht, Netherlands: Springer Netherlands, 2023
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-186810 (URN)10.1007/s11118-022-10027-8 (DOI)000817859500001 ()2-s2.0-85133012690 (Scopus ID)
Available from: 2022-07-04 Created: 2022-07-04 Last updated: 2024-11-19Bibliographically approved
Björn, A., Björn, J. & Latvala, V. (2023). The Dirichlet Problem for p-minimizers on Finely Open Sets in Metric Spaces. Potential Analysis, 59, 1117-1140
Open this publication in new window or tab >>The Dirichlet Problem for p-minimizers on Finely Open Sets in Metric Spaces
2023 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 59, p. 1117-1140Article in journal (Refereed) Published
Abstract [en]

We initiate the study of fine p-(super)minimizers, associated with p-harmonic functions, on finely open sets in metric spaces, where infinity. After having developed their basic theory, we obtain the p-fine continuity of the solution of the Dirichlet problem on a finely open set with continuous Sobolev boundary values, as a by-product of similar pointwise results. These results are new also on unweighted . We build this theory in a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality.

Place, publisher, year, edition, pages
Springer, 2023
Keywords
Dirichlet problem; Doubling measure; Fine continuity; Fine p-minimizer; Fine p-superminimizer; Fine supersolution; Finely open set; Metric space; Nonlinear fine potential theory; Poincare inequality; Quasiopen set
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-185264 (URN)10.1007/s11118-022-09996-7 (DOI)000792530600001 ()
Note

Funding Agencies|Linkoping University; Swedish Research Council [2016-03424, 2020-04011, 621-2014-3974, 2018-04106]

Available from: 2022-05-24 Created: 2022-05-24 Last updated: 2023-11-02Bibliographically approved
Björn, A., Björn, J. & Lehrback, J. (2023). Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions. Journal d'Analyse Mathematique, 150, 159-214
Open this publication in new window or tab >>Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions
2023 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 150, p. 159-214Article in journal (Refereed) Published
Abstract [en]

In a complete metric space equipped with a doubling measure supporting a p-Poincare inequality, we prove sharp growth and integrability results for p-harmonic Green functions and their minimal p-weak upper gradients. We show that these properties are determined by the growth of the underlying measure near the singularity. Corresponding results are obtained also for more general p-harmonic functions with poles, as well as for singular solutions of elliptic differential equations in divergence form on weighted R-n and on manifolds.The proofs are based on a new general capacity estimate for annuli, which implies precise pointwise estimates for p-harmonic Green functions. The capacity estimate is valid under considerably milder assumptions than above. We also use it, under these milder assumptions, to characterize singletons of zero capacity and the p-parabolicity of the space. This generalizes and improves earlier results that have been important especially in the context of Riemannian manifolds.

Place, publisher, year, edition, pages
HEBREW UNIV MAGNES PRESS, 2023
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-193387 (URN)10.1007/s11854-023-0273-4 (DOI)000958727800007 ()
Available from: 2023-05-05 Created: 2023-05-05 Last updated: 2024-03-21Bibliographically approved
Björn, A., Björn, J. & Shanmugalingam, N. (2022). Classification of metric measure spaces and their ends using p-harmonic functions. Annales Fennici Mathematici, 47(2), 1025-1052
Open this publication in new window or tab >>Classification of metric measure spaces and their ends using p-harmonic functions
2022 (English)In: Annales Fennici Mathematici, ISSN 2737-0690, Vol. 47, no 2, p. 1025-1052Article in journal (Refereed) Published
Abstract [en]

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite p-energy p-harmonic and p-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local p-Poincare inequality. Similar classifications have earlier been obtained for Riemann surfaces and Riemannian manifolds. We study the inclusions between these classes of metric measure spaces, and their relationship to the p-hyperbolicity of the metric space and its ends. In particular, we characterize spaces that carry nonconstant p-harmonic functions with finite p-energy as spaces having at least two well-separated p-hyperbolic sequences of sets towards infinity. We also show that every such space X has a function f is an element of/ LP(X) + R with finite p-energy.

Place, publisher, year, edition, pages
SUOMALAINEN TIEDEAKATEMIA, 2022
Keywords
Classification of metric measure spaces; doubling measure; end at infinity; finite p-energy; p-hyperbolic sequence; Liouville theorem; p-harmonic function; Poincare inequality; p-parabolic; quasiharmonic function; quasiminimizer
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-194067 (URN)10.54330/afm.120618 (DOI)001075076000020 ()2-s2.0-85135858654 (Scopus ID)
Available from: 2023-05-23 Created: 2023-05-23 Last updated: 2025-02-27
Asratian, A., Björn, A. & Turesson, B.-O. (2020). Diskret matematik (1ed.). Stockholm: Liber
Open this publication in new window or tab >>Diskret matematik
2020 (Swedish)Book (Other academic)
Abstract [sv]

Den här boken är främst avsedd för grundläggande kurser i diskret matematik vid universitet och högskolor. Framför allt riktar den sig till första- och andraårsstudenter på data-, matematik-, civilingenjörs- och högskoleingenjörsprogrammen.

Place, publisher, year, edition, pages
Stockholm: Liber, 2020. p. 338 Edition: 1
Keywords
Diskret matematik
National Category
Discrete Mathematics
Identifiers
urn:nbn:se:liu:diva-170494 (URN)9789147133581 (ISBN)
Note

Upplaga 1

Available from: 2020-10-13 Created: 2020-10-13 Last updated: 2020-10-21Bibliographically approved
Björn, A. & Hansevi, D. (2019). Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces. Analysis and Geometry in Metric Spaces, 7(1), 179-196
Open this publication in new window or tab >>Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces
2019 (English)In: Analysis and Geometry in Metric Spaces, E-ISSN 2299-3274, Vol. 7, no 1, p. 179-196Article in journal (Refereed) Published
Abstract [en]

The theory of boundary regularity for p-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincare inequality, 1 amp;lt; p amp;lt; infinity. The barrier classification of regular boundary points is established, and it is shown that regularity is a local property of the boundary. We also obtain boundary regularity results for solutions of the obstacle problem on open sets, and characterize regularity further in several other ways.

Place, publisher, year, edition, pages
Walter de Gruyter, 2019
Keywords
barrier; boundary regularity; Kellogg property; metric space; obstacle problem; p-harmonic function
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-163060 (URN)10.1515/agms-2019-0009 (DOI)000501996600001 ()2-s2.0-85076097518 (Scopus ID)
Note

Funding Agencies|Swedish Research CouncilSwedish Research Council [2016-03424]

Available from: 2020-01-09 Created: 2020-01-09 Last updated: 2020-02-10Bibliographically approved
Arnlind, J., Björn, A. & Björn, J. (2016). An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces. Nonlinear Analysis, 134, 70-104
Open this publication in new window or tab >>An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces
2016 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 134, p. 70-104Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD, 2016
Keywords
Dirichlet problem; First eigenvalue; Generalized Sobolev space; Gradient relation; Lattice; Metric space; Noncommutative function; Obstacle problem; Operator-valued function; Partial order; Poincare set; Rayleigh quotient; Rellich-Kondrachov cone; Trace class ideal; Variational problem
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-126128 (URN)10.1016/j.na.2015.12.010 (DOI)000370489300004 ()
Note

Funding Agencies|Swedish Research Council

Available from: 2016-03-15 Created: 2016-03-15 Last updated: 2017-11-30
Björn, A. (2016). HbA1c according to different standards. Linköping: Matematiska institutionen, Linköpings Universitet
Open this publication in new window or tab >>HbA1c according to different standards
2016 (English)Other (Other (popular science, discussion, etc.))
Place, publisher, year, pages
Linköping: Matematiska institutionen, Linköpings Universitet, 2016. p. 4
Keywords
HbA1c, diabetics
National Category
Endocrinology and Diabetes
Identifiers
urn:nbn:se:liu:diva-146039 (URN)
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2018-04-03Bibliographically approved
Björn, A. (2016). HbA1c enligt olika standarder. Linköping: Matematiska institutionen, Linköpings Universitet
Open this publication in new window or tab >>HbA1c enligt olika standarder
2016 (Swedish)Other (Other (popular science, discussion, etc.))
Place, publisher, year, pages
Linköping: Matematiska institutionen, Linköpings Universitet, 2016. p. 4
Keywords
HbA1c, diabetics
National Category
Endocrinology and Diabetes
Identifiers
urn:nbn:se:liu:diva-146037 (URN)
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2018-04-03Bibliographically approved
Björn, A. (2016). HbA1c podle různých standardů;. Linköping: Matematiska institutionen, Linköpings Universitet
Open this publication in new window or tab >>HbA1c podle různých standardů;
2016 (Czech)Other (Other (popular science, discussion, etc.))
Place, publisher, year, pages
Linköping: Matematiska institutionen, Linköpings Universitet, 2016. p. 4
National Category
Endocrinology and Diabetes
Identifiers
urn:nbn:se:liu:diva-146040 (URN)
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2018-04-03Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9677-8321

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