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Variational Analysis in Sobolev and BV Spaces
Applications to PDEs and Optimization, Second Edition
Gerard Michaille , Giuseppe Buttazzo , Hedy Attouch
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.
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