Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (MPS-SIAM Series on Optimization)

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9780898716009: Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (MPS-SIAM Series on Optimization)

This self-contained book is excellent for graduate-level courses devoted to variational analysis, optimization, and partial differential equations (PDEs). It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization is not just for students, however; it is a comprehensive guide for anyone who wants to approach the field of variational analysis in a systematic way, starting from the most classical examples and working up to a research level. This book also contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references. Organized in a way that makes it accessible to a large audience, the book is divided into two parts. In Part I, classical Sobolev spaces are introduced and the reader is provided with the basic tools and methods of variational analysis and optimization in infinite dimensional spaces, with applications to classical PDE problems. The last chapters in Part I introduce finite element methods and spectral analysis methods, the two most powerful tools that allow the computation of approximate solutions of variational problems. In Part II, BV(W) spaces are introduced and new trends in variational analysis are presented. In this part the reader is introduced to the flexibility of variational methods.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Book Description :

A detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. It contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references.

About the Author :

Hedy Attouch is Professor of Mathematics at Université Montpellier II, France. He is Director of Laboratoire d'Analyse Convexe and of ACSIOM (the analysis, computational, and optimization component of the Institute of Mathematics and Modelization of Montpellier). He has published 100 articles and has supervised 23 theses in the fields of variational analysis and optimization. Giuseppe Buttazzo is Professor of Mathematics at Università di Pisa. He is an editor of several international journals and author of more than 130 scientific articles and 16 books. He has supervised 13 theses in the fields of calculus of variations, nonlinear PDEs, control theory, and related topics. Gérard Michaille is Professor at Centre Universitaire de Formation et de Recherche at Nîmes (CUFR) and a member of the UMR-CNRS I3S of the Mathematical Department at Université Montpellier II, France. He works in the fields of variational analysis and homogenization and their applications in mechanics.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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Attouch, Hedy, Buttazzo, Giuseppe, Micha
Edité par SIAM, Society for Industrial a (2005)
ISBN 10 : 0898716004 ISBN 13 : 9780898716009
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Hedy Attouch; Giuseppe Buttazzo; Gérard Michaille
Edité par SIAM, Society for Industrial and Applied Mathematics (2005)
ISBN 10 : 0898716004 ISBN 13 : 9780898716009
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Hedy Attouch, Giuseppe Buttazzo, Gérard Michaille
Edité par SIAM, Society for Industrial and Applied Mathematics (2005)
ISBN 10 : 0898716004 ISBN 13 : 9780898716009
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Description du livre SIAM, Society for Industrial and Applied Mathematics, 2005. Paperback. État : New. N° de réf. du libraire DADAX0898716004

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Hedy Attouch; Giuseppe Buttazzo; Gérard Michaille
Edité par SIAM, Society for Industrial and Applied Mathematics (2005)
ISBN 10 : 0898716004 ISBN 13 : 9780898716009
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Description du livre SIAM, Society for Industrial and Applied Mathematics, 2005. Paperback. État : New. book. N° de réf. du libraire 0898716004

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Hedy Attouch; Giuseppe Buttazzo; Gérard Michaille
Edité par SIAM, Society for Industrial and Applied Mathematics (2005)
ISBN 10 : 0898716004 ISBN 13 : 9780898716009
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