Optimal doubling, reifenberg flatness and operators of p-laplace type

Avelin, Benny (author): Umeå universitet,Institutionen för matematik och matematisk statistik

Lundström, Niklas L.P. (author): Umeå universitet,Institutionen för matematik och matematisk statistik

Nyström, Kaj (author): Umeå universitet,Institutionen för matematik och matematisk statistik

(creator_code:org_t)

Elsevier BV, 2011
2011
English.
In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 74:17, s. 5943-5955

Related links:: https://umu.diva-por... (primary) (Raw object); show more...; http://umu.diva-port...; https://uu.diva-port... (primary) (Raw object); https://urn.kb.se/re...; https://doi.org/10.1...; https://urn.kb.se/re...; show less...

Abstract Subject headings

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 x∈Rn and η∈Rn∖{0}. Let Ω⊂Rn 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 Ω∖D in the weak sense. We extend to Rn∖Ω by putting on Rn∖Ω. 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.

About the subject

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.