Coverart for item
The Resource Sobolev spaces : with applications to elliptic partial differential equations, Vladimir Mazʹia ; [translated from Russian by Tatyana O. Shaposhnikova]

Sobolev spaces : with applications to elliptic partial differential equations, Vladimir Mazʹia ; [translated from Russian by Tatyana O. Shaposhnikova]

Label
Sobolev spaces : with applications to elliptic partial differential equations
Title
Sobolev spaces
Title remainder
with applications to elliptic partial differential equations
Statement of responsibility
Vladimir Mazʹia ; [translated from Russian by Tatyana O. Shaposhnikova]
Creator
Contributor
Subject
Language
  • eng
  • rus
  • eng
Summary
"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 {uFB01}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 differential equations. New historical comments, five new chapters and a signi{uFB01}cantly augmented list of references aim to create a broader and modern view of the area."--Publisher's website
Member of
Cataloging source
IXA
http://library.link/vocab/creatorName
Mazʹi︠a︡, V. G
Dewey number
515.782
Illustrations
illustrations
Index
index present
Language note
Translated from the Russian
LC call number
QA323
LC item number
.M3813 2011
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Shaposhnikova, T. O
Series statement
Grundlehren der mathematischen Wissenschaften
Series volume
342
http://library.link/vocab/subjectName
Sobolev spaces
Label
Sobolev spaces : with applications to elliptic partial differential equations, Vladimir Mazʹia ; [translated from Russian by Tatyana O. Shaposhnikova]
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 803-847) and indexes
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Basic Properties of Sobolev Spaces -- Inequalities for Functions Vanishing at the Boundary -- Conductor and Capacitary Inequalities with Applications to Sobolev-Type Embeddings -- Generalizations for Functions on Manifolds and Topological Spaces -- Integrability of Functions in the Space L [superscript 1] [subscript 1] [omega] -- Integrability of Functions in the Space L [superscript 1] [subscript p] [omega] -- Continuity and Boundedness of Functions in Sobolev Spaces -- Localization Moduli of Sobolev Embeddings for General Domains -- Space of Functions of Bounded Variation -- Certain Function Spaces, Capacities, and Potentials -- Capacitary and Trace Inequalities for Functions in R [superscript n] with Derivatives of an Arbitrary Order -- Pointwise Interpolation Inequalities for Derivatives and Potentials -- A Variant of Capacity -- Integral Inequality for Functions on a Cube -- Embedding of the Space L[̊superscript l] [subscript p] [omega] into Other Function Spaces -- Embedding L[̊superscript l] [subscript p] [omega],[nu] [subset of] W[superscript m] [subscript r] [omega] -- Approximation in Weighted Sobolev Spaces -- Spectrum of the Schrödinger Operator and the Dirichlet Laplacian
Control code
708263933
Dimensions
25 cm
Edition
2nd, rev. and augmented ed.
Extent
xxviii, 866 pages
Isbn
9783642155642
Isbn Type
(e-ISBN)
Lccn
2011921122
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)708263933
Label
Sobolev spaces : with applications to elliptic partial differential equations, Vladimir Mazʹia ; [translated from Russian by Tatyana O. Shaposhnikova]
Publication
Bibliography note
Includes bibliographical references (pages 803-847) and indexes
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Basic Properties of Sobolev Spaces -- Inequalities for Functions Vanishing at the Boundary -- Conductor and Capacitary Inequalities with Applications to Sobolev-Type Embeddings -- Generalizations for Functions on Manifolds and Topological Spaces -- Integrability of Functions in the Space L [superscript 1] [subscript 1] [omega] -- Integrability of Functions in the Space L [superscript 1] [subscript p] [omega] -- Continuity and Boundedness of Functions in Sobolev Spaces -- Localization Moduli of Sobolev Embeddings for General Domains -- Space of Functions of Bounded Variation -- Certain Function Spaces, Capacities, and Potentials -- Capacitary and Trace Inequalities for Functions in R [superscript n] with Derivatives of an Arbitrary Order -- Pointwise Interpolation Inequalities for Derivatives and Potentials -- A Variant of Capacity -- Integral Inequality for Functions on a Cube -- Embedding of the Space L[̊superscript l] [subscript p] [omega] into Other Function Spaces -- Embedding L[̊superscript l] [subscript p] [omega],[nu] [subset of] W[superscript m] [subscript r] [omega] -- Approximation in Weighted Sobolev Spaces -- Spectrum of the Schrödinger Operator and the Dirichlet Laplacian
Control code
708263933
Dimensions
25 cm
Edition
2nd, rev. and augmented ed.
Extent
xxviii, 866 pages
Isbn
9783642155642
Isbn Type
(e-ISBN)
Lccn
2011921122
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)708263933

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