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© 2000

Elements of Nonlinear Analysis

Textbook

Part of the Birkhäuser Advanced Texts book series (BAT)

Table of contents

  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 95-103
  8. Michel Chipot
    Pages 105-129
  9. Michel Chipot
    Pages 131-143
  10. Michel Chipot
    Pages 145-183
  11. Michel Chipot
    Pages 185-205
  12. Michel Chipot
    Pages 207-220
  13. Michel Chipot
    Pages 221-250
  14. Back Matter
    Pages 251-256

About this book

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

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland

Bibliographic information

  • Book Title Elements of Nonlinear Analysis
  • Authors Michel Chipot
  • Series Title Birkhäuser Advanced Texts
  • DOI https://doi.org/10.1007/978-3-0348-8428-0
  • Copyright Information Birkhäuser Basel 2000
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-6406-9
  • Softcover ISBN 978-3-0348-9563-7
  • eBook ISBN 978-3-0348-8428-0
  • Edition Number 1
  • Number of Pages VII, 256
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Functional Analysis
    Partial Differential Equations
  • Buy this book on publisher's site

Reviews

"This is a relatively formal book which starts out as a motivational chapter introducing two examples, elasticity and diffusion, of the application of nonlinear analysis. Aimed mainly at graduate students and nonspecialists, the material is then developed in a largely abstract fashion, introducing topics in existence, uniqueness, regularity and approximation for elliptic and parabolic problems."   --Aslib Book Guide

"This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the intricacies of the more esoteric ones…it encompass[es] many methods of dynamical systems in quite simple and original settings. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications."   --Mathematical Reviews