# Elements of Nonlinear Analysis

• Michel Chipot
Textbook

Part of the Birkhäuser Advanced Texts book series (BAT)

1. Front Matter
Pages i-vii
2. Michel Chipot
Pages 1-14
3. Michel Chipot
Pages 15-38
4. Michel Chipot
Pages 39-48
5. Michel Chipot
Pages 49-58
6. Michel Chipot
Pages 59-83
7. Michel Chipot
Pages 85-94
8. Michel Chipot
Pages 95-103
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Pages 105-129
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Pages 131-143
11. Michel Chipot
Pages 145-183
12. Michel Chipot
Pages 185-205
13. Michel Chipot
Pages 207-220
14. Michel Chipot
Pages 221-250
15. Back Matter
Pages 251-256

### Introduction

The goal of this book is to present some modern aspects of nonlinear analysis. Some of the material introduced is classical, some more exotic. We have tried to emphasize simple cases and ideas more than complicated refinements. Also, as far as possible, we present proofs that are not classical or not available in the usual literature. Of course, only a small part of nonlinear analysis is covered. Our hope is that the reader - with the help of these notes - can rapidly access the many different aspects of the field. We start by introducing two physical issues: elasticity and diffusion. The pre­ sentation here is original and self contained, and helps to motivate all the rest of the book. Then we turn to some theoretical material in analysis that will be needed throughout (Chapter 2). The next six chapters are devoted to various aspects of elliptic problems. Starting with the basics of the linear theory, we introduce a first type of nonlinear problem that has today invaded the whole mathematical world: variational inequalities. In particular, in Chapter 6, we introduce a simple theory of regularity for nonlocal variational inequalities. We also attack the question of the existence, uniqueness and approximation of solutions of quasilinear and mono­ tone problems (see Chapters 5, 7, 8). The material needed to read these parts is contained in Chapter 2. The arguments are explained using the simplest possible examples.

### Keywords

Calculus of Variations Distribution Euler–Lagrange equation Numerical analysis applied mathematics finite element method functional analysis

#### Authors and affiliations

• Michel Chipot
• 1
1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-0348-8428-0
• Copyright Information Birkhäuser Basel 2000
• Publisher Name Birkhäuser, Basel
• eBook Packages
• Print ISBN 978-3-0348-9563-7
• Online ISBN 978-3-0348-8428-0
• Buy this book on publisher's site