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Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1238-6751
2015 (English)In: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, no 1, 161-214 p.Article in journal (Refereed) Published
Abstract [en]

We study the double obstacle problem for p-harmonic functions on arbitrary bounded nonopen sets E in quite general metric spaces. The Dirichlet and single obstacle problems are included as special cases. We obtain the Adams criterion for the solubility of the single obstacle problem and establish connections with fine potential theory. We also study when the minimal p-weak upper gradient of a function remains minimal when restricted to a nonopen subset. Many of the results are new even for open E (apart from those which are trivial in this case) and also on R-n.

Place, publisher, year, edition, pages
Universidad Autonoma de Madrid, Departamento de Matematicas / European Mathematical Society , 2015. Vol. 31, no 1, 161-214 p.
Keyword [en]
Adams criterion; Dirichlet problem; doubling measure; fine potential theory; Friedrichs inequality; metric space; minimal upper gradient; nonlinear; obstacle problem; p-harmonic; Poincare inequality; potential theory; upper gradient
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-117820DOI: 10.4171/RMI/830ISI: 000352568500007OAI: oai:DiVA.org:liu-117820DiVA: diva2:811246
Note

Funding Agencies|Swedish Research Council

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

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Björn, AndersBjörn, Jana
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