The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications

Björn, Anders; Björn, Jana; Sjödin, Tomas

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The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications

Björn, Anders

Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9677-8321

Björn, Jana

Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1238-6751

Sjödin, Tomas

Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.

2018 (English)In: Revista matemática iberoamericana, ISSN 0213-2230, E-ISSN 2235-0616, Vol. 34, no 3, p. 1323-1360Article in journal (Refereed) Published

Abstract [en]

We study the Dirichlet problem for p-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new approach to the invariance problem we introduce Sobolev-Perron solutions. We obtain various resolutivity and invariance results, and also show that most functions that have earlier been proved to be resolutive are in fact Sobolev-resolutive. We also introduce (Sobolev)-Wiener solutions and harmonizability in this nonlinear context, and study their connections to (Sobolev)-Perron solutions, partly using Q-compactifications.

Place, publisher, year, edition, pages

EUROPEAN MATHEMATICAL SOC , 2018. Vol. 34, no 3, p. 1323-1360

Keywords [en]

Dirichlet problem; harmonizable; invariance; metric space; nonlinear potential theory; Perron solution; p-harmonic function; Q-compactification; quasicontinuous; resolutive; Wiener solution

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Mathematical Analysis

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URN: urn:nbn:se:liu:diva-151225DOI: 10.4171/RMI/1025ISI: 000442889700015OAI: oai:DiVA.org:liu-151225DiVA, id: diva2:1248000

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Funding Agencies|Swedish Research Council [621-2011-3139, 621-2014-3974]

Available from: 2018-09-13 Created: 2018-09-13 Last updated: 2018-09-13

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Björn, Anders

Björn, Jana

Sjödin, Tomas

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