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Birkhäuser

Elements of Nonlinear Analysis

  • Textbook
  • © 2000

Overview

Authors:
  1. Michel Chipot

    1. Institut für Mathematik, Universität Zürich, Zürich, Switzerland

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Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-vii
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  2. Some Physical Motivations

    • Michel Chipot
    Pages 1-14

  3. A Short Background in Functional Analysis

    • Michel Chipot
    Pages 15-38

  4. Elliptic Linear Problems

    • Michel Chipot
    Pages 39-48

  5. Elliptic Variational Inequalities

    • Michel Chipot
    Pages 49-58

  6. Nonlinear Elliptic Problems

    • Michel Chipot
    Pages 59-83

  7. A Regularity Theory for Nonlocal Variational Inequalities

    • Michel Chipot
    Pages 85-94

  8. Uniqueness and Nonuniqueness Issues

    • Michel Chipot
    Pages 95-103

  9. Finite Element Methods for Elliptic Problems

    • Michel Chipot
    Pages 105-129

  10. Minimizers

    • Michel Chipot
    Pages 131-143

  11. Minimizing Sequences

    • Michel Chipot
    Pages 145-183

  12. Linear Parabolic Equations

    • Michel Chipot
    Pages 185-205

  13. Nonlinear Parabolic Problems

    • Michel Chipot
    Pages 207-220

  14. Asymptotic Analysis

    • Michel Chipot
    Pages 221-250

  15. Back Matter

    Pages 251-256
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Keywords

About this book

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

Authors and Affiliations

  • Institut für Mathematik, Universität Zürich, Zürich, Switzerland

    Michel Chipot

Bibliographic Information

  • Book Title: Elements of Nonlinear Analysis

  • Authors: Michel Chipot

  • Series Title: Birkhäuser Advanced Texts Basler Lehrbücher

  • DOI: https://doi.org/10.1007/978-3-0348-8428-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2000

  • Hardcover ISBN: 978-3-7643-6406-9Published: 01 November 2000

  • Softcover ISBN: 978-3-0348-9563-7Published: 31 October 2012

  • eBook ISBN: 978-3-0348-8428-0Published: 06 December 2012

  • Series ISSN: 1019-6242

  • Series E-ISSN: 2296-4894

  • Edition Number: 1

  • Number of Pages: VII, 256

  • Topics: Functional Analysis, Partial Differential Equations

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