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SOBOLEV SPACES, FINE GRADIENTS AND QUASICONTINUITY ON QUASIOPEN SETS
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.
2016 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 41, no 2, 551-560 p.Article in journal (Refereed) PublishedText
Abstract [en]

We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space X equipped with a doubling measure supporting a p-Poincare inequality with 1 amp;lt; p amp;lt; infinity, and connect them to the Sobolev theory in R-n. In particular, we show that for quasiopen subsets of R-n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpelainen and Maly in 1992.

Place, publisher, year, edition, pages
SUOMALAINEN TIEDEAKATEMIA , 2016. Vol. 41, no 2, 551-560 p.
Keyword [en]
Fine gradient; fine topology; metric space; minimal upper gradient; Newtonian space; quasicontinuous; quasiopen; Sobolev space
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-130151DOI: 10.5186/aasfm.2016.4130ISI: 000378014700003OAI: oai:DiVA.org:liu-130151DiVA: diva2:948528
Note

Funding Agencies|Swedish Research Council; Linkoping University; Institut Mittag-Leffler in the autumn

Available from: 2016-07-12 Created: 2016-07-11 Last updated: 2016-07-12

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Björn, AndersBjörn, Jana
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