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Titlebook: Sobolev Spaces; with Applications to Vladimir Maz‘ya Book 2011Latest edition Springer-Verlag Berlin Heidelberg 2011 46E35, 42B37, 26D10.Sob

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發(fā)表于 2025-3-21 17:38:53 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Sobolev Spaces
副標(biāo)題with Applications to
編輯Vladimir Maz‘ya
視頻videohttp://file.papertrans.cn/870/869247/869247.mp4
概述New, expanded and revised edition of Sobolev Spaces, originally published in the Springer Series in Soviet Mathematics (1985) Is enhanced by many recent results New applications to linear and nonlinea
叢書名稱Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Sobolev Spaces; with Applications to Vladimir Maz‘ya Book 2011Latest edition Springer-Verlag Berlin Heidelberg 2011 46E35, 42B37, 26D10.Sob
描述Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume ?rst appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differe
出版日期Book 2011Latest edition
關(guān)鍵詞46E35, 42B37, 26D10; Sobolev spaces; general domains; integral inequalities; isoperimetric and isocapaci
版次2
doihttps://doi.org/10.1007/978-3-642-15564-2
isbn_softcover978-3-662-51729-1
isbn_ebook978-3-642-15564-2Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 2011
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沙發(fā)
發(fā)表于 2025-3-21 22:02:15 | 只看該作者
Localization Moduli of Sobolev Embeddings for General Domains,nstants. To describe our results we need to introduce some notation that will be frequently used in this chapter..We supply . with the norm . where ? stands for the gradient and . is a nonempty open set with compact closure .. It is standard that a change of . leads to an equivalent norm in .. . . ..
板凳
發(fā)表于 2025-3-22 04:03:11 | 只看該作者
地板
發(fā)表于 2025-3-22 07:20:45 | 只看該作者
0072-7830 many recent results New applications to linear and nonlineaSobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theor
5#
發(fā)表于 2025-3-22 10:56:46 | 只看該作者
Book 2011Latest editionhematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theor
6#
發(fā)表于 2025-3-22 13:01:18 | 只看該作者
Basic Properties of Sobolev Spaces,in the book. In Sect.?1.3 a complete study of the one-dimensional Hardy inequality with two weights is presented. The case of a weight of unrestricted sign on the left-hand side is also included here, following Maz’ya and Verbitsky (Function Spaces, Interpolation Theory and Related Topics, pp.?369–3
7#
發(fā)表于 2025-3-22 19:44:34 | 只看該作者
,Inequalities for Functions Vanishing at?the?Boundary,e in .. Here we consider inequalities with the integral . on the right-hand side. The function .(.,.), defined for .∈. and .∈?., is positive homogeneous of degree one in .. The conditions are stated in terms of isoperimetric (for .=1 in Sect.?2.1) and isocapacitary (for .≥1, in Sects.?2.2–2.4) inequ
8#
發(fā)表于 2025-3-23 00:25:01 | 只看該作者
9#
發(fā)表于 2025-3-23 02:40:11 | 只看該作者
,Generalizations for Functions on Manifolds and?Topological Spaces,ended to much more general situtations; the present chapter only touches such opportunities..Applications to estimates of the principal eigenvalue of the Dirichlet Laplacian on a Riemannian manifold are presented in Sects.?4.2 and?4.3. In Sects.?4.4–4.6 we derive some conductor inequalities for func
10#
發(fā)表于 2025-3-23 08:47:49 | 只看該作者
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