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]
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The item Sobolev spaces : with applications to elliptic partial differential equations, Vladimir Mazʹia ; [translated from Russian by Tatyana O. Shaposhnikova] represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Sobolev spaces : with applications to elliptic partial differential equations, Vladimir Mazʹia ; [translated from Russian by Tatyana O. Shaposhnikova] represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 TeubnerTexte 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
 Language

 eng
 rus
 eng
 Edition
 2nd, rev. and augmented ed.
 Extent
 xxviii, 866 pages
 Contents

 Basic Properties of Sobolev Spaces
 Inequalities for Functions Vanishing at the Boundary
 Conductor and Capacitary Inequalities with Applications to SobolevType 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
 Isbn
 9783642155642
 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]
 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 TeubnerTexte 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
 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]
 Bibliography note
 Includes bibliographical references (pages 803847) 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 SobolevType 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
 (eISBN)
 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]
 Bibliography note
 Includes bibliographical references (pages 803847) 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 SobolevType 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
 (eISBN)
 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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