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.

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.

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 .

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

Keywords

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

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

Organisations

Linköping University, Department of Mathematics, Mathematics and Applied Mathematics

Linköping University, The Institute of Technology (Closed down 2015-05-19)