Birkhäuser Advanced Texts Basler Lehrbücher

Elements of Nonlinear Analysis

Authors: Chipot, Michel

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About this Textbook

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.

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


Table of contents (13 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-0348-8428-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-3-7643-6406-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-3-0348-9563-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Elements of Nonlinear Analysis
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
2000
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8428-0
DOI
10.1007/978-3-0348-8428-0
Hardcover ISBN
978-3-7643-6406-9
Softcover ISBN
978-3-0348-9563-7
Series ISSN
1019-6242
Edition Number
1
Number of Pages
VII, 256
Topics