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Adamowicz, Tomasz
Publications (2 of 2) Show all publications
Adamowicz, T., Björn, A. & Björn, J. (2014). Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points. Annales de l'Institut Henri Poincare. Analyse non linéar, 31(6), 1131-1153
Open this publication in new window or tab >>Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points
2014 (English)In: 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) Published
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.

Place, publisher, year, edition, pages
Elsevier Masson / Institute Henri Poincar�, 2014
Comparison principle; Kellogg property; Isc-regularized; Nonlinear potential theory; Nonstandard growth equation; Obstacle problem; p(.)-harmonic; Quasicontinuous; Regular boundary point; Removable singularity; Semiregular point; Sobolev space; Strongly irregular point; p(.)-superharmonic; p(.)-supersolution; Trichotomy; Variable exponent
National Category
urn:nbn:se:liu:diva-113374 (URN)10.1016/j.anihpc.2013.07.012 (DOI)000346550400003 ()

Funding Agencies|Swedish Research Council

Available from: 2015-01-16 Created: 2015-01-16 Last updated: 2017-12-05
Adamowicz, T., Björn, A., Björn, J. & Shanmugalingam, N. (2013). Prime ends for domains in metric spaces. Advances in Mathematics, 238, 459-505
Open this publication in new window or tab >>Prime ends for domains in metric spaces
2013 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 238, p. 459-505Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2013
Accessibility, Almost John domain, Capacity, Doubling measure, End, Finitely connected at the boundary, John domain, Locally connected, Mazurkiewicz distance, Metric space, p-modulus, Poincare inequality, Prime end, Uniform domain
National Category
Natural Sciences
urn:nbn:se:liu:diva-92601 (URN)10.1016/j.aim.2013.01.014 (DOI)000317089200013 ()

Funding Agencies|Swedish Research Council||Swedish Fulbright Commission||Charles Phelps Taft Research Center at the University of Cincinnati||Taft Research Center||Simons Foundation|200474|

Available from: 2013-05-16 Created: 2013-05-14 Last updated: 2017-12-06

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