Product of extension domains is still an extension domain

Pekka Koskela; Zheng Zhu

doi:10.1512/iumj.2020.69.8366

Product of extension domains is still an extension domain

Pekka Koskela
, Zheng Zhu

University of Jyväskylä

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

2 Scopus citations

Abstract

Our main result gives a functional property of the class of W^1,p-extension domains. Let Ω₁ ⊆ ℝⁿ and Ω₂ ⊆ ℝ^m both be W^1,p-extension domains for some 1 < p ≤ ∞. We prove that Ω₁ × Ω₂ ⊆ ℝ^n+m is also a W^1,p-extension domain. We also establish the converse statement.

Original language	English
Pages (from-to)	137-150
Number of pages	14
Journal	Indiana University Mathematics Journal
Volume	69
Issue number	1
DOIs	https://doi.org/10.1512/iumj.2020.69.8366
State	Published - 2020
Externally published	Yes

Keywords

Product
Sobolev extension

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10.1512/iumj.2020.69.8366

Cite this

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title = "Product of extension domains is still an extension domain",

abstract = "Our main result gives a functional property of the class of W1,p-extension domains. Let Ω1 ⊆ ℝn and Ω2 ⊆ ℝm both be W1,p-extension domains for some 1 < p ≤ ∞. We prove that Ω1 × Ω2 ⊆ ℝn+m is also a W1,p-extension domain. We also establish the converse statement.",

keywords = "Product, Sobolev extension",

author = "Pekka Koskela and Zheng Zhu",

note = "Publisher Copyright: {\textcopyright} 2020 Indiana University Mathematics Journal.",

year = "2020",

doi = "10.1512/iumj.2020.69.8366",

language = "英语",

volume = "69",

pages = "137--150",

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publisher = "Department of Mathematics, Indiana University",

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T1 - Product of extension domains is still an extension domain

AU - Koskela, Pekka

AU - Zhu, Zheng

PY - 2020

Y1 - 2020

N2 - Our main result gives a functional property of the class of W1,p-extension domains. Let Ω1 ⊆ ℝn and Ω2 ⊆ ℝm both be W1,p-extension domains for some 1 < p ≤ ∞. We prove that Ω1 × Ω2 ⊆ ℝn+m is also a W1,p-extension domain. We also establish the converse statement.

AB - Our main result gives a functional property of the class of W1,p-extension domains. Let Ω1 ⊆ ℝn and Ω2 ⊆ ℝm both be W1,p-extension domains for some 1 < p ≤ ∞. We prove that Ω1 × Ω2 ⊆ ℝn+m is also a W1,p-extension domain. We also establish the converse statement.

KW - Product

KW - Sobolev extension

UR - https://www.scopus.com/pages/publications/85084478604

U2 - 10.1512/iumj.2020.69.8366

DO - 10.1512/iumj.2020.69.8366

M3 - 文章

AN - SCOPUS:85084478604

SN - 0022-2518

VL - 69

SP - 137

EP - 150

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 1

ER -

Product of extension domains is still an extension domain

Abstract

Keywords

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