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Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, Second Edition

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by Hedy Attouch, Giuseppe Buttazzo, Gérard Michaille


2014 / xii + 793 pages / Hardcover / ISBN: 978-1-611973-47-1 / List Price $145.50 / MOS/SIAM Member Price $101.85 / Order Code MO17

Keywords: variational analysis, calculus of variations, optimization, Sobolev spaces, partial differential equations

Preface to the Second Edition
Preface to the First Edition


SIREV Book Review

This second edition replaces Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (MP06, ISBN 978-0-898716-00-9), which is no longer available.

This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision.

This second edition covers several new topics:

  • new section on capacity theory and elements of potential theory now includes the concepts of quasi-open sets and quasi-continuity,
  • increased number of examples in the areas of linearized elasticity system, obstacles problems, convection-diffusion, and semilinear equations,
  • new section on mass transportation problems and the Kantorovich relaxed formulation of the Monge problem,
  • new subsection on stochastic homogenization establishes the mathematical tools coming from ergodic theory, and
  • an entirely new and comprehensive chapter (17) devoted to gradient flows and the dynamical approach to equilibria.

The book is intended for Ph.D. students, researchers, and practitioners who want to approach the field of variational analysis in a systematic way.

About the Authors
Hedy Attouch is a professor in the Institut de Mathématique et de Modélisation de Montpellier II, where he also has been director of the Laboratory of Convex Analysis and of ACSIOM. His research focuses on variational analysis, convex analysis, continuous optimization, semialgebraic optimization, gradient flows, the interaction among these fields of research, and their applications. He has published more than 100 articles in international journals and has written 6 books. He serves as editor for several journals on continuous optimization and is responsible for several international research programs.

Giuseppe Buttazzo is a professor in the Department of Mathematics at the University of Pisa. He has been a keynote speaker at many international conferences and workshops on the fields of calculus of variations, nonlinear PDEs, applied mathematics, control theory, and related topics. He is the author of more than 180 scientific publications and 20 books, and he serves as an editor of several international journals.

Gérard Michaille is a professor at the University of Nîmes and member of the UMR-CNRS Institut de Mathématique et de Modélisation de Montpellier. He works in the areas of variational analysis, homogenization, and the applications of PDEs in mechanics and physics.


ISBN: 9781611973471

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