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Poincare inequalities and Newtonian Sobolev functions on noncomplete 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
2019 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 266, no 1, p. 44-69Article in journal (Refereed) Published
Abstract [en]

Let X be a noncomplete metric measure space satisfying the usual (local) assumptions of a doubling property and a Poincare inequality. We study extensions of Newtonian Sobolev functions to the completion (X) over cap of X and use them to obtain several results on X itself, in particular concerning minimal weak upper gradients, Lebesgue points, quasicontinuity, regularity properties of the capacity and better Poincare inequalities. We also provide a discussion about possible applications of the completions and extension results to p-harmonic functions on noncomplete spaces and show by examples that this is a rather delicate issue opening for various interpretations and new investigations. (C) 2018 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2019. Vol. 266, no 1, p. 44-69
Keywords [en]
Lebesgue point; Noncomplete metric space; Newtonian Sobolev space; p-harmonic function; Poincare inequality; Quasiminimizer
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-152794DOI: 10.1016/j.jde.2018.07.029ISI: 000449108500002OAI: oai:DiVA.org:liu-152794DiVA, id: diva2:1265304
Note

Funding Agencies|Swedish Research Council [621-2014-3974, 2016-03424]

Available from: 2018-11-22 Created: 2018-11-22 Last updated: 2018-11-22

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Björn, AndersBjörn, Jana
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  • harvard1
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  • Other style
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  • de-DE
  • en-GB
  • en-US
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  • nn-NB
  • sv-SE
  • Other locale
More languages
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