Partial Differential Equations 2

Functional Analytic Methods

  • Friedrich Sauvigny

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Friedrich Sauvigny
    Pages 1-31
  3. Friedrich Sauvigny
    Pages 33-129
  4. Friedrich Sauvigny
    Pages 131-190
  5. Friedrich Sauvigny
    Pages 191-260
  6. Friedrich Sauvigny
    Pages 261-304
  7. Friedrich Sauvigny
    Pages 305-366
  8. Friedrich Sauvigny
    Pages 367-443
  9. Back Matter
    Pages 445-453

About this book

Introduction

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.

In this second volume, special emphasis is placed on functional analytic methods and applications to differential geometry. The following topics are treated:

  • solvability of operator equations in Banach spaces 
  • linear operators in Hilbert spaces and spectral theory
  • Schauder's theory of linear elliptic differential equations
  • weak solutions of differential equations 
  • nonlinear partial differential equations and characteristics
  • nonlinear elliptic systems
  • boundary value problems from differential geometry

This new second edition of this volume has been thoroughly revised and a new chapter on boundary value problems from differential geometry has been added.

In the first volume, partial differential equations by integral representations are treated in a classical way.

This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study.

Keywords

Monge-Ampère equations Schauder's continuity method degree of mapping in Banach spaces nonlinear elliptic systems and H-surfaces spectral theory weak solutions and regularity

Authors and affiliations

  • Friedrich Sauvigny
    • 1
  1. 1.Mathematical InstituteBrandenburgian Technical UniversityCottbusGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-2984-4
  • Copyright Information Springer-Verlag London 2012
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-2983-7
  • Online ISBN 978-1-4471-2984-4
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book