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Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-9677-8321
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-1238-6751
2006 (English)In: Journal of the Mathematical Society of Japan, ISSN 0025-5645, E-ISSN 1881-1167, Vol. 58, no 4, 1211-1232 p.Article in journal (Refereed) Published
Abstract [en]

We study p-harmonic functions in complete metric spaces equipped with a doubling Borel measure supporting a weak (1, p)-Poincaré inequality, 1 < p < ∞. We establish the barrier classification of regular boundary points from which it also follows that regularity is a local property of the boundary. We also prove boundary regularity at the fixed (given) boundary for solutions of the one-sided obstacle problem on bounded open sets. Regularity is further characterized in several other ways. Our results apply also to Cheeger p-harmonic functions and in the Euclidean setting to script A sign-harmonic functions, with the usual assumptions on script A sign.

Place, publisher, year, edition, pages
2006. Vol. 58, no 4, 1211-1232 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-35887DOI: 10.2969/jmsj/1179759546Local ID: 28912OAI: oai:DiVA.org:liu-35887DiVA: diva2:256735
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13

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Björn, AndersBjörn, Jana

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