Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions on metric spaces
2008 (English)In: Houston Journal of Mathematics, ISSN 0362-1588, Vol. 34, no 4, 1197-1211 p.Article in journal (Refereed) Published
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.
Density, Lipschitz function, metric space, Newtonian function, Newton-Sobolev function, outer capacity, Poincare inequality, quasicontinuous
IdentifiersURN: urn:nbn:se:liu:diva-17616OAI: oai:DiVA.org:liu-17616DiVA: diva2:210912