The volume of the boundary of a Sobolev (p,q)-extension domain

Pekka Koskela, Alexander Ukhlov, Zheng Zhu

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1 Scopus citations

Abstract

Let n≥2 and 1≤q<p<∞. We prove that if Ω⊂Rn is a Sobolev (p,q)-extension domain, with additional capacitary restrictions on the boundary in the case q≤n−1, n>2, then |∂Ω|=0. In the case 1≤q<n−1, we give an example of a Sobolev (p,q)-extension domain with |∂Ω|>0.

Original languageEnglish
Article number109703
JournalJournal of Functional Analysis
Volume283
Issue number12
DOIs
StatePublished - 15 Dec 2022

Keywords

  • Ahlfors regular
  • Boundary volume
  • Capacity estimate
  • Sobolev extension

ASJC Scopus subject areas

  • Analysis

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