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

Pekka Koskela; Alexander Ukhlov; Zheng Zhu

doi:10.1016/j.jfa.2022.109703

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

Pekka Koskela, Alexander Ukhlov, Zheng Zhu

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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 language	American English
Article number	109703
Journal	Journal of Functional Analysis
Volume	283
Issue number	12
DOIs	https://doi.org/10.1016/j.jfa.2022.109703
State	Published - 15 Dec 2022

Keywords

Ahlfors regular
Boundary volume
Capacity estimate
Sobolev extension

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/j.jfa.2022.109703

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

abstract = "Let n≥2 and 1≤qn 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≤q0.",

keywords = "Ahlfors regular, Boundary volume, Capacity estimate, Sobolev extension",

author = "Pekka Koskela and Alexander Ukhlov and Zheng Zhu",

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year = "2022",

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doi = "10.1016/j.jfa.2022.109703",

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AU - Koskela, Pekka

AU - Ukhlov, Alexander

AU - Zhu, Zheng

PY - 2022/12/15

Y1 - 2022/12/15

N2 - Let n≥2 and 1≤qn 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≤q0.

AB - Let n≥2 and 1≤qn 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≤q0.

KW - Ahlfors regular

KW - Boundary volume

KW - Capacity estimate

KW - Sobolev extension

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U2 - 10.1016/j.jfa.2022.109703

DO - 10.1016/j.jfa.2022.109703

M3 - Article

SN - 0022-1236

VL - 283

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 12

M1 - 109703

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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