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

Pekka Koskela, Alexander Ukhlov, Zheng Zhu

Research output: Working paper/PreprintPreprint

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Abstract

Let n ≥ 2 and 1 ≤ q < p < ∞. We prove that if Ω ⊂ Rn is a Sobolev
(p, q)-extension domain, with additional capacitory restrictions on 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 GB
StatePublished - 14 Dec 2020

Keywords

  • math.AP
  • math.FA

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