Mathematical Preliminaries.- Variational Equations.- Multivalued Variational Equations.- Variational Inequalities.- Hemivariational Inequalities.- Variational-Hemivariational Inequalities.
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.
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.
This is the first research monograph to focus on variational inequalities as part of nonsmooth variational systems research. The authors discuss partial differential equations, variational equations, variational and hemivariational inequalities, and related topics. With a wealth of problems and techniques from nonlinear and nonsmooth analysis, this versatile text is an important reference for mathematicians working in analysis, partial differential equations, elasticity, materials science and mechanics applications, as well as for physicists and engineers. It can serve as a main or supplemental text for a variety of specialized nonlinear analysis courses.