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Functional analysis, Sobolev spaces ...

Brézis, H.

Functional analysis, Sobolev spaces and partial differential equations /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Functional analysis, Sobolev spaces and partial differential equations // Haim Brezis.
作者:	Brézis, H.
其他作者:	Brézis, H.
出版者:	New York ;Springer, : c2011.,
面頁冊數:	xiii, 599 p. :ill. ; : 24 cm.;
附註:	Originally published in French as Analyse fonctionelle, théorie et applications (Paris: Masson, c1983) ; this English edition contains revisions and added exercises.
標題:	Sobolev spaces. -
ISBN:	9780387709130 (pbk.) :

Functional analysis, Sobolev spaces and partial differential equations /
Brézis, H.

Functional analysis, Sobolev spaces and partial differential equations /Haim Brezis. - New York ;Springer,c2011. - xiii, 599 p. :ill. ;24 cm. - Universitext. - Universitext..

Originally published in French as Analyse fonctionelle, théorie et applications (Paris: Masson, c1983) ; this English edition contains revisions and added exercises.

Includes bibliographical references (p. 585-594) and index.

The Hahn-Banach theorems : introduction to the theory of conjugate convex functions -- The uniform boundedness principle and the closed graph theorem -- Weak topologies, reflexive spaces, separable spaces, uniform convexity -- Lp spaces -- Hilbert spaces -- Compact operators, spectral decomposition of self-adjoint compact operators -- The Hille-Yosida theorem -- Sobolev spaces and the variational formulation of boundary value problems in one dimension -- Sobolev spaces and the variational formulation of elliptic boundary value problems in N dimensions -- Evolution problems : the heat equation and the wave equation -- Miscellaneous complements

Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct "worlds," functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research.

ISBN: 9780387709130 (pbk.) :NT2602

LCCN: 2010938382

Nat. Bib. No.: GBA9A9553bnb

Nat. Bib. Agency Control No.: 015415972UkSubjects--Topical Terms:

528664
Sobolev spaces.

LC Class. No.: QA320 / .B73 2011

Dewey Class. No.: 515.7

Functional analysis, Sobolev spaces and partial differential equations /
LDR:03529cam a2200337 a 4500 001 756484
003 DLC
005 20130402182628.0
008 130912s2011 nyua b 001 0 eng
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015 $a GBA9A9553 $2 bnb
016 7 $a 015415972 $2 Uk
020 $a 9780387709130 (pbk.) : $c NT2602
020 $a 0387709134 (pbk.)
020 $a 9780387709147 (e-ISBN)
020 $a 0387709142 (e-ISBN)
035 $a (OCoLC)ocn717212864
035 $a 2010938382
040 $a UKM $b eng $c CHRRO $d OCLCQ $d UKM $d BTCTA $d YDXCP $d OHX $d CDX $d RBN $d GZM $d DGU $d NHM $d AZU $d DLC $d NFU
042 $a lccopycat
050 0 0 $a QA320 $b .B73 2011
082 0 4 $a 515.7 $2 22
100 1 $a Brézis, H. $q (Haim) $3 915233
245 1 0 $a Functional analysis, Sobolev spaces and partial differential equations / $c Haim Brezis.
260 $a New York ; $a London : $c c2011. $b Springer,
300 $a xiii, 599 p. : $b ill. ; $c 24 cm.
490 1 $a Universitext
500 $a Originally published in French as Analyse fonctionelle, théorie et applications (Paris: Masson, c1983) ; this English edition contains revisions and added exercises.
504 $a Includes bibliographical references (p. 585-594) and index.
505 0 $a The Hahn-Banach theorems : introduction to the theory of conjugate convex functions -- The uniform boundedness principle and the closed graph theorem -- Weak topologies, reflexive spaces, separable spaces, uniform convexity -- Lp spaces -- Hilbert spaces -- Compact operators, spectral decomposition of self-adjoint compact operators -- The Hille-Yosida theorem -- Sobolev spaces and the variational formulation of boundary value problems in one dimension -- Sobolev spaces and the variational formulation of elliptic boundary value problems in N dimensions -- Evolution problems : the heat equation and the wave equation -- Miscellaneous complements
520 $a Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct "worlds," functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research.
520 8 $a This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of die important Analyse Fonctionnelle (1983). Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English version is a welcome addition to this list.
520 8 $a The first part of the text deals with abstract results in FA and operator theory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specific differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theory of PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs which arise, for example, in differential geometry, harmonic analysis, engineering, mechanics, physics etc. and belong in the toolbox of any graduate student studying analysis.
650 0 $a Sobolev spaces. $3 528664
650 0 $a Differential equations, Partial. $3 527784
650 0 $a Functional analysis. $3 527706
700 1 $a Brézis, H. $q (Haim) $3 915233
830 0 $a Universitext. $3 881573