uu.seUppsala University Publications

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Optimal doubling, Reifenberg flatness and operators of p-Laplace typePrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2011 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 17, p. 5943-5955Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2011. Vol. 74, no 17, p. 5943-5955
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-163435DOI: 10.1016/j.na.2011.05.061OAI: oai:DiVA.org:uu-163435DiVA, id: diva2:463936
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true}); Available from: 2012-11-30 Created: 2011-12-12 Last updated: 2017-12-08Bibliographically approved
##### In thesis

In this paper we consider operators of p-Laplace type of the form ∇·A(x,∇u) = 0. ConcerningA we assume, for p ∈ (1,∞) fixed, an appropriate ellipticity type condition, H¨older continuityin x and that A(x, ) = ||p−1A(x, /||) whenever x ∈ Rn and ∈ Rn \ {0}. Let ⊂ Rn be abounded domain, let D be a compact subset of . We say that ˆu = ˆup,D, is the A-capacitaryfunction for D in if ˆu ≡ 1 on D, ˆu ≡ 0 on @ in the sense of W1,p0 () and ∇·A(x,∇ˆu) = 0 in \D in the weak sense. We extend ˆu to Rn \ by putting ˆu ≡ 0 on Rn \ . Then there existsa unique finite positive Borel measure ˆμ on Rn, with support in @, such thatZ hA(x,∇ˆu),∇i dx = −Z dˆμ whenever ∈ C∞0 (Rn \ D).In this paper we prove that if is Reifenberg flat with vanishing constant, thenlimr→0infw∈∂ˆμ(B(w, r))ˆμ(B(w, r))= limr→0supw∈∂ˆμ(B(w, r))ˆμ(B(w, r))= n−1,for every , 0 < ≤ 1. In particular, we prove that ˆμ is an asymptotically optimal doublingmeasure on @.

1. Boundary Behavior of *p*-Laplace Type Equations$(function(){PrimeFaces.cw("OverlayPanel","overlay615186",{id:"formSmash:j_idt733:0:j_idt737",widgetVar:"overlay615186",target:"formSmash:j_idt733:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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