© 2012

Partial Differential Equations 2

Functional Analytic Methods

  • Provides a complete and thorough introduction into the theory of linear and nonlinear partial differential equations

  • Presents interesting applications to physics and differential geometry

  • Includes the basic methods from linear and nonlinear functional analysis


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


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.


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

  1. 1.Mathematical InstituteBrandenburgian Technical UniversityCottbusGermany

Bibliographic information

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From the reviews of the second edition:

“The second volume of the revised edition of this book presents functional analytic methods and applications to problems in differential geometry. … The book will be a useful addition to the libraries of all those interested in the theory and applications of partial differential equations.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1246, 2012)