Nonsmooth Variational Problems and Their Inequalities (eBook)

Comparison Principles and Applications

Siegfried Carl, Vy Khoi Le, Dumitru Motreanu (Autoren)

eBook Download: PDF

2007 | 1. Auflage
398 Seiten
Springer-Verlag
978-0-387-46252-3 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 7.6.2007
• Reihe/Serie: Springer Monographs in Mathematics
• Reihe/Serie: Springer Monographs in Mathematics
• Zusatzinfo: X, 398 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik
• Schlagworte: Boundary value problem • differential equation • Functional Analysis • Mathematica • partial differential equation • Partial differential equations
• ISBN-10: 0-387-46252-X / 038746252X
• ISBN-13: 978-0-387-46252-3 / 9780387462523