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Критерий соболевской корректности задачи Дирихле для уравнения Пуассона в липшицевых областях. II Full article

Journal Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Output data Year: 2023, Volume: 20, Number: 1, Pages: 211-244 Pages count : 34 DOI: 10.33048/semi.2023.20.018
Tags approximative numbers, Dirichlet problem for the Poisson equation, Hardy type inequality, Lipschitz domain, straightening
Authors Парфёнов А.И. 1
Affiliations
1 Sobolev Institute of Mathematics

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0008

Abstract: We study the Dirichlet problem for the Poisson equation in bounded Lipschitz domains. We show that its well-posedness in the higher order Sobolev space implies a discrete Hardy type inequality that contains a positive harmonic function with vanishing trace and the approximative numbers of the boundary of the domain. This necessary condition is also expected to be su cient for the well-posedness. A simpler condition occurring in the author's straightenability theory of Lipschitz domains is shown to be equivalent to the existence of a homeomorphism that straightens the boundary and preserves with respect to composition the subspace of zero trace functions in the considered Sobolev space.
Cite: Парфёнов А.И.
Критерий соболевской корректности задачи Дирихле для уравнения Пуассона в липшицевых областях. II
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. Т.20. №1. С.211-244. DOI: 10.33048/semi.2023.20.018 WOS Scopus РИНЦ
Dates:
Submitted: May 3, 2022
Published print: Mar 13, 2023
Published online: Mar 13, 2023
Identifiers:
Web of science: WOS:000959070400012
Scopus: 2-s2.0-85150778955
Elibrary: 54768290
Citing:
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Scopus 1
Web of science 1
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