Elliptic Partial Differential Equations of Second Order

  • David Gilbarg
  • Neil S. Trudinger

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 224)

Table of contents

  1. Front Matter
    Pages i-x
  2. Introduction

    1. David Gilbarg, Neil S. Trudinger
      Pages 1-9
  3. Linear Equations

    1. Front Matter
      Pages 11-11
    2. David Gilbarg, Neil S. Trudinger
      Pages 13-29
    3. David Gilbarg, Neil S. Trudinger
      Pages 30-49
    4. David Gilbarg, Neil S. Trudinger
      Pages 50-67
    5. David Gilbarg, Neil S. Trudinger
      Pages 68-81
    6. David Gilbarg, Neil S. Trudinger
      Pages 82-136
    7. David Gilbarg, Neil S. Trudinger
      Pages 137-165
    8. David Gilbarg, Neil S. Trudinger
      Pages 166-200
  4. Quasilinear Equations

    1. Front Matter
      Pages 201-201
    2. David Gilbarg, Neil S. Trudinger
      Pages 203-220
    3. David Gilbarg, Neil S. Trudinger
      Pages 221-238
    4. David Gilbarg, Neil S. Trudinger
      Pages 239-263
    5. David Gilbarg, Neil S. Trudinger
      Pages 264-277
    6. David Gilbarg, Neil S. Trudinger
      Pages 278-299
    7. David Gilbarg, Neil S. Trudinger
      Pages 300-327
    8. David Gilbarg, Neil S. Trudinger
      Pages 328-380
  5. Back Matter
    Pages 381-404

About this book

Introduction

This volume is intended as an essentially self contained exposition of portions of the theory of second order quasilinear elliptic partial differential equations, with emphasis on the Dirichlet problem in bounded domains. It grew out of lecture notes for graduate courses by the authors at Stanford University, the final material extending well beyond the scope of these courses. By including preparatory chapters on topics such as potential theory and functional analysis, we have attempted to make the work accessible to a broad spectrum of readers. Above all, we hope the readers of this book will gain an appreciation of the multitude of ingenious barehanded techniques that have been developed in the study of elliptic equations and have become part of the repertoire of analysis. Many individuals have assisted us during the evolution of this work over the past several years. In particular, we are grateful for the valuable discussions with L. M. Simon and his contributions in Sections 15.4 to 15.8; for the helpful comments and corrections of J. M. Cross, A. S. Geue, J. Nash, P. Trudinger and B. Turkington; for the contributions of G. Williams in Section 10.5 and of A. S. Geue in Section 10.6; and for the impeccably typed manuscript which resulted from the dedicated efforts oflsolde Field at Stanford and Anna Zalucki at Canberra. The research of the authors connected with this volume was supported in part by the National Science Foundation.

Keywords

differential equation functional analysis partial differential equation potential theory

Authors and affiliations

  • David Gilbarg
    • 1
  • Neil S. Trudinger
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of Pure MathematicsAustralian National UniversityCanberraAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-96379-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1977
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-96381-0
  • Online ISBN 978-3-642-96379-7
  • Series Print ISSN 0072-7830
  • About this book