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The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1238-6751
University of Cincinnati, OH 45221 USA.
2015 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 7, 3078-3114 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier , 2015. Vol. 259, no 7, 3078-3114 p.
Keyword [en]
Dirichlet problem; Finite connectivity at the boundary; Mazurkiewicz distance; Metric space; p-harmonic function; Perron method
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-120434DOI: 10.1016/j.jde.2015.04.014ISI: 000357903500018OAI: oai:DiVA.org:liu-120434DiVA: diva2:845705
Note

Funding Agencies|Swedish Research Council; Swedish Fulbright Commission; Charles Phelps Taft Research Center at the University of Cincinnati; Taft Research Center; Simons Foundation [200474]; NSF grant [DMS-1200915]

Available from: 2015-08-12 Created: 2015-08-11 Last updated: 2016-05-04

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Björn, AndersBjörn, Jana
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