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Partial Differential Equations 1

Foundations and Integral Representations

  • Friedrich Sauvigny

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Friedrich Sauvigny
    Pages 1-90
  3. Friedrich Sauvigny
    Pages 91-173
  4. Friedrich Sauvigny
    Pages 175-214
  5. Friedrich Sauvigny
    Pages 215-304
  6. Friedrich Sauvigny
    Pages 305-361
  7. Friedrich Sauvigny
    Pages 363-438
  8. Back Matter
    Pages 439-447

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 first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated:

• integration and differentiation on manifolds

• foundations of functional analysis

• Brouwer's mapping degree

• generalized analytic functions

• potential theory and spherical harmonics

• linear partial differential equations

This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added.

The second volume will present functional analytic methods and applications to problems in differential geometry.

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

Poisson's equation and spherical harmonics generalized integral theorems inhomogeneous Cauchy-Riemann equation maximum and comparison principles modern function spaces wave equation

Authors and affiliations

  • Friedrich Sauvigny
    • 1
  1. 1.Mathematical Institute, LS AnalysisBrandenburgian Technical UniversityCottbusGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-2981-3
  • Copyright Information Springer-Verlag London 2012
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-2980-6
  • Online ISBN 978-1-4471-2981-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site