Carl / Motreanu Nonsmooth Variational Problems and Their Inequalities

Comparison Principles and Applications
1. Auflage 2007
ISBN: 978-0-387-46252-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 398 Seiten

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.

Autoren/Hrsg.

Carl, Siegfried

Motreanu, Dumitru

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;1 Introduction;11
4;2 Mathematical Preliminaries;21
4.1;2.1 Basic Functional Analysis;21
4.2;2.2 Sobolev Spaces;38
4.3;2.3 Operators of Monotone Type;49
4.4;2.4 First-Order Evolution Equations;59
4.5;2.5 Nonsmooth Analysis;73
5;3 Variational Equations;91
5.1;3.1 Semilinear Elliptic Equations;91
5.2;3.2 Quasilinear Elliptic Equations;103
5.3;3.3 Quasilinear Parabolic Equations;115
5.4;3.4 Sign-Changing Solutions via Fucik Spectrum;133
5.5;3.5 Quasilinear Elliptic Problems of Periodic Type;144
5.6;3.6 Notes and Comments;151
6;4 Multivalued Variational Equations;153
6.1;4.1 Motivation and Introductory Examples;153
6.2;4.2 Inclusions with Global Growth on Clarke’s Gradient;165
6.3;4.3 Inclusions with Local Growth on Clarke’s Gradient;177
6.4;4.4 Application: Difference of Multifunctions;190
6.5;4.5 Parabolic Inclusions with Local Growth;200
6.6;4.6 An Alternative Concept of Sub-Supersolutions;218
6.7;4.7 Notes and Comments;219
7;5 Variational Inequalities;221
7.1;5.1 Variational Inequalities on Closed Convex Sets;223
7.2;5.2 Variational Inequalities with Convex Functionals;244
7.3;5.3 Evolutionary Variational Inequalities;256
7.4;5.4 Sub-Supersolutions and Monotone Penalty Approximations;267
7.5;5.5 Systems of Variational Inequalities;277
7.6;5.6 Notes and Comments;287
8;6 Hemivariational Inequalities;289
8.1;6.1 Notion of Sub-Supersolution;291
8.2;6.2 Quasilinear Elliptic Hemivariational Inequalities;295
8.3;6.3 Evolutionary Hemivariational Inequalities;309
8.4;6.4 Notes and Comments;326
9;7 Variational–Hemivariational Inequalities;329
9.1;7.1 Elliptic Variational–Hemivariational Inequalities;329
9.2;7.2 Evolution Variational–Hemivariational Inequalities;346
9.3;7.3 Nonsmooth Critical Point Theory;365
9.4;7.4 A Constraint Hemivariational Inequality;372
9.5;7.5 Eigenvalue Problem for a Variational– Hemivariational Inequality;378
9.6;7.6 Notes and Comments;385
10;List of Symbols;388
11;References;390
12;Index;401