Synopses & Reviews
This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.
Review
From the reviews: "This monograph presents in a systematic way the method of sub- and supersolutions for solving variational and hemivariational inequalities. ... Each chapter begins with a short overview presenting cases and ideas, and concludes with notes and remarks giving references to the literature. ... It is carefully written and suitable for advanced graduate students and researchers having a good background in functional analysis, basic partial differential equations, and critical point theory." (Thomas Bartsch, Mathematical Reviews, Issue, 2007 i) "This monograph contains seven chapters, the bibliography of 223 entries, and an index. ... This well-written book contains large number of material. It can be useful for graduate students and researchers interested in variational methods. In the beginning of each chapter the authors give some motivation for the material of the chapter." (Alexander G. Ramm, Zentralblatt MATH, Vol. 1109 (11), 2007) "The present monograph develops in a careful and thorough way the theory of sub- and supersolutions for variational equalities and inequalities. ... The book is an important addition to the literature on nonlinear analysis, convex analysis, variational and hemivariational inequalities, nonlinear elliptic and parabolic partial differential equations, elasticity theory, fracture mechanics, and general obstacle and unilateral problems; it will be a welcome addition to the libraries of researchers and students of these areas." (Klaus Schmitt, SIAM Review, Vol. 49 (3), 2007)
Table of Contents
Preface.- 1. Introduction.- 2. Mathematical Preliminaries.- 3. Variational Equations.- 4. Multivalued Variational Equations.- 5. Variational Inequalities.- 6. Hemivariational Inequalities.- 7. Variational-Hemivariational Inequalities.- List of Symbols.- References.- Index.