: Siegfried Carl, Vy K. Le, Dumitru Motreanu
: Nonsmooth Variational Problems and Their Inequalities Comparison Principles and Applications
: Springer-Verlag
: 9780387462523
: 1
: CHF 89.50
:
: Analysis
: English
: 395
: Wasserzeichen
: PC/MAC/eReader/Tablet
: PDF

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.
Preface5
Contents7
1 Introduction11
2 Mathematical Preliminaries21
2.1 Basic Functional Analysis21
2.2 Sobolev Spaces38
2.3 Operators of Monotone Type49
2.4 First-Order Evolution Equations59
2.5 Nonsmooth Analysis73
3 Variational Equations91
3.1 Semilinear Elliptic Equations91
3.2 Quasilinear Elliptic Equations103
3.3 Quasilinear Parabolic Equations115
3.4 Sign-Changing Solutions via Fucik Spectrum133
3.5 Quasilinear Elliptic Problems of Periodic Type144
3.6 Notes and Comments151
4 Multivalued Variational Equations153
4.1 Motivation and Introductory Examples153
4.2 Inclusions with Global Growth on Clarke’s Gradient165
4.3 Inclusions with Local Growth on Clarke’s Gradient177
4.4 Application: Difference of Multifunctions190
4.5 Parabolic Inclusions with Local Growth200
4.6 An Alternative Concept of Sub-Supersolutions218
4.7 Notes and Comments219
5 Variational Inequalities221
5.1 Variational Inequalities on Closed Convex Sets223
5.2 Variational Inequalities with Convex Functionals244
5.3 Evolutionary Variational Inequalities256
5.4 Sub-Supersolutions and Monotone Penalty Approximations267
5.5 Systems of Variational Inequalities277
5.6 Notes and Comments287
6 Hemivariational Inequalities289
6.1 Notion of Sub-Supersolution291
6.2 Quasilinear Elliptic Hemivariational Inequalities295
6.3 Evolutionary Hemivariational Inequalities309
6.4 Notes and Comments326
7 Variational–Hemivariational Inequalities329
7.1 Elliptic Variational–Hemivariational Inequalities329
7.2 Evolution Variational–Hemivariational Inequalities346
7.3 Nonsmooth Critical Point Theory365
7.4 A Constraint Hemivariational Inequality372
7.5 Eigenvalue Problem for a Variational– Hemivariational Inequality378
7.6 Notes and Comments385
List of Symbols388
References390
Index401