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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 243, Pages 213–229
(Mi tm429)
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This article is cited in 3 scientific papers (total in 3 papers)
Strengthened Sobolev Spaces for Domains with Irregular Boundary
E. G. D'yakonov M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Abstract:
The properties of strengthened Sobolev spaces $G^{1,m}\equiv G^{1,m}(\Omega ;S)$, $m\geq 1/2$, are studied. These spaces are constructed on the basis of the classical space $W_2^1(\Omega )\equiv H^1(\Omega )$ for a bounded plane domain $\Omega$ whose boundary $\Gamma$ is not, in general, Lipschitzian; $S\subset \bar\Omega\equiv\Omega\cup \Gamma$; and $S=\bar S$ consists of finitely many smooth arcs. Special attention is given to situations when either a singular point of the boundary (the definition is given below) belongs to $S$ or two arcs from $S$ are tangent at their common endpoint, whereby the interior angle between them is zero. Characteristics of traces on $S$ and $\Gamma$ are obtained that make it possible to prove not only an extension theorem but also theorems on approximation of elements from $G^{1,1}$ and their traces by smooth functions.
Received in October 2002
Citation:
E. G. D'yakonov, “Strengthened Sobolev Spaces for Domains with Irregular Boundary”, Function spaces, approximations, and differential equations, Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS, Trudy Mat. Inst. Steklova, 243, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 213–229; Proc. Steklov Inst. Math., 243 (2003), 204–219
Linking options:
https://www.mathnet.ru/eng/tm429 https://www.mathnet.ru/eng/tm/v243/p213
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Abstract page: | 397 | Full-text PDF : | 116 | References: | 76 |
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