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The Weak Cartan Property for the p-fine Topology on 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: 0000-0002-1238-6751
University of Eastern Finland, Finland.
2015 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 64, no 3, 915-941 p.Article in journal (Refereed) Published
Abstract [en]

We study the p-fine topology on complete metric spaces equipped with a doubling measure supporting a p-Poincare inequality, 1 less than p less than infinity. We establish a weak Cartan property, which yields characterizations of the p-thinness and the p-fine continuity, and allows us to show that the p-fine topology is the coarsest topology making all p-superharmonic functions continuous. Our p-harmonic and superharmonic functions are defined by means of scalar-valued upper gradients, and do not rely on a vector-valued differentiable structure.

Place, publisher, year, edition, pages
INDIANA UNIV MATH JOURNAL , 2015. Vol. 64, no 3, 915-941 p.
Keyword [en]
Capacity; coarsest topology; doubling; fine topology finely continuous; metric space; p-harmonic; Poincare inequality; quasi-continuous; superharmonic; thick; thin; weak Cartan property; Wiener criterion
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-120665ISI: 000358271700009OAI: oai:DiVA.org:liu-120665DiVA: diva2:847541
Note

Funding Agencies|Swedish Research Council; Scandinavian Research Network Analysis and Application,; Linkopings universitet

Available from: 2015-08-20 Created: 2015-08-20 Last updated: 2017-12-04

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