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 |
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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 |
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Affiliations |
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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
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 |