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Optimal doubling, reifenberg flatness and operators of p-laplace type
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 17, 5943-5955 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider equations of p-Laplace type of the form A(x,u)=0. Concerning A we assume, for p∈(1,) fixed, an appropriate ellipticity type condition, Hölder continuity in x and that A(x,η)=|η|p−1A(x,η/|η|) whenever xRn and ηRn∖{0}. Let ΩRn be a bounded domain, let D be a compact subset of Ω. We say that is the A-capacitary function for D in Ω if on D, on Ω in the sense of and in ΩD in the weak sense. We extend to RnΩ by putting on RnΩ. Then there exists a unique finite positive Borel measure on Rn, with support in Ω, such that In this paper, we prove that if Ω is Reifenberg flat with vanishing constant, then for every τ, 0<τ≤1. In particular, we prove that is an asymptotically optimal doubling measure on Ω.

Place, publisher, year, edition, pages
2011. Vol. 74, no 17, 5943-5955 p.
Keyword [en]
Reifenberg flat domain, Reifenberg flat domain with vanishing constant, p-harmonic function, A-harmonic function, Variable coefficients, Doubling measure, Asymptotically optimal doubling measure
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-22721DOI: 10.1016/j.na.2011.05.061ISI: 000293784500011OAI: oai:DiVA.org:umu-22721DiVA: diva2:217752
Funder
Swedish Research Council, VR-70629701
Available from: 2009-05-15 Created: 2009-05-15 Last updated: 2015-03-17Bibliographically approved

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Avelin, BennyLundström, Niklas L.P.Nyström, Kaj

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