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.
Among the new elements in this second edition: the section of Chapter 5 on capacity theory and elements of potential theory now includes the concepts of quasi-open sets and quasi-continuity; Chapter 6 includes an increased number of examples in the areas of linearized elasticity system, obstacles problems, convection-diffusion, and semilinear equations; Chapter 11 has been expanded to include a section on mass transportation problems and the Kantorovich relaxed formulation of the Monge problem; a new subsection on stochastic homogenization in Chapter 12 establishes the mathematical tools coming from ergodic theory, and illustrates them in the scope of statistically homogeneous materials; Chapter 16 has been augmented by examples illustrating the shape optimization procedure; and Chapter 17 is an entirely new and comprehensive chapter devoted to gradient flows and the dynamical approach to equilibria.
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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Maße
Höhe: 260 mm
Breite: 183 mm
Dicke: 44 mm
Gewicht
ISBN-13
978-1-61197-347-1 (9781611973471)
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Schweitzer Klassifikation
Hedy Attouch is a professor in the Institut de Mathematique et de Modelisation 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 six 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. Gerard Michaille is a professor at the University of Nimes and member of the UMR-CNRS Institut de Mathematique et de Modelisation de Montpellier. He works in the areas of variational analysis, homogenization, and the applications of PDEs in mechanics and physics.
Chapter 1: Introduction
Part I: Basic Variational Principles
Chapter 2: Weak Solution Methods in Variational Analysis
Chapter 3: Abstract Variational Principles
Chapter 4: Complements on Measure Theory
Chapter 5: Sobolev Spaces
Chapter 6: Variational Problems: Some Classical Examples
Chapter 7: The Finite Element Method
Chapter 8: Spectral Analysis of the Laplacian
Chapter 9: Convex Duality and Optimization
Part II: Advanced Variational Analysis
Chapter 10: Spaces BV and SBV
Chapter 11: Relaxation in Sobolev, BV, and Young Measures Spaces
Chapter 12: ?-convergence and Applications
Chapter 13: Integral Functionals of the Calculus of Variations
Chapter 14: Applications in Mechanics and Computer Vision
Chapter 15: Variational Problems with a Lack of Coercivity
Chapter 16: An Introduction to Shape Optimization Problems
Chapter 17: Gradient Flows