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Nonlinear balayage on metric spaces
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1238-6751
University of Jyväskylä.
Helsinki University of Technology.
2009 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, no 5-6, 2153-2171 p.Article in journal (Refereed) Published
Abstract [en]

We develop a theory of balayage on complete doubling metric measure spaces supporting a Poincaré inequality. In particular, we are interested in continuity and p-harmonicity of the balayage. We also study connections to the obstacle problem. As applications, we characterize regular boundary points and polar sets in terms of balayage.

Place, publisher, year, edition, pages
2009. Vol. 71, no 5-6, 2153-2171 p.
Keyword [en]
Balayage; Boundary regularity; Continuity; Doubling measure; Metric space; Nonlinear; Obstacle problem; Perron solution; p-harmonic; Polar set; Poincaré inequality; Potential theory; Superharmonic
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-19049DOI: 10.1016/j.na.2009.01.051OAI: oai:DiVA.org:liu-19049DiVA: diva2:222823
Note
Original Publication: Anders Björn, Jana Björn, Tero Mäkäläinen and Mikko Parviainen, Nonlinear balayage on metric spaces, 2009, Nonlinear Analysis, (71), 5-6, 2153-2171. http://dx.doi.org/10.1016/j.na.2009.01.051 Copyright: Elsevier Science B.V., Amsterdam. http://www.elsevier.com/ Available from: 2009-06-11 Created: 2009-06-09 Last updated: 2017-12-13Bibliographically approved

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