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Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions 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 Cincinnati.
2008 (English)In: Houston Journal of Mathematics, ISSN 0362-1588, Vol. 34, no 4, 1197-1211 p.Article in journal (Refereed) Published
Abstract [en]

We show that on complete doubling metric measure spaces X supporting a Poincare inequality, all Newton-Sobolev functions u are quasicontinuous, i.e. that for every epsilon > 0 there is an open set U subset of X such that C-p(U) < epsilon and the restriction of u to X\U is continuous. This implies that the capacity is an outer capacity.

Place, publisher, year, edition, pages
2008. Vol. 34, no 4, 1197-1211 p.
Keyword [en]
Density, Lipschitz function, metric space, Newtonian function, Newton-Sobolev function, outer capacity, Poincare inequality, quasicontinuous
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-17616OAI: oai:DiVA.org:liu-17616DiVA: diva2:210912
Available from: 2009-04-07 Created: 2009-04-06 Last updated: 2017-12-13

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Björn, AndersBjörn, Jana

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