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Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces
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: 0000-0002-2902-3279
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. Vol. 7, no 1, p. 179-196
Keywords [en]
barrier; boundary regularity; Kellogg property; metric space; obstacle problem; p-harmonic function
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-163060DOI: 10.1515/agms-2019-0009ISI: 000501996600001Scopus ID: 2-s2.0-85076097518OAI: oai:DiVA.org:liu-163060DiVA, id: diva2:1384227
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

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