Advertisement

Classical Potential Theory

  • David H. Armitage
  • Stephen J. Gardiner

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. David H. Armitage, Stephen J. Gardiner
    Pages 1-32
  3. David H. Armitage, Stephen J. Gardiner
    Pages 33-58
  4. David H. Armitage, Stephen J. Gardiner
    Pages 59-88
  5. David H. Armitage, Stephen J. Gardiner
    Pages 89-121
  6. David H. Armitage, Stephen J. Gardiner
    Pages 123-162
  7. David H. Armitage, Stephen J. Gardiner
    Pages 163-195
  8. David H. Armitage, Stephen J. Gardiner
    Pages 197-232
  9. David H. Armitage, Stephen J. Gardiner
    Pages 233-272
  10. David H. Armitage, Stephen J. Gardiner
    Pages 273-304
  11. Back Matter
    Pages 305-333

About this book

Introduction

From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises. The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine topology, the Martin boundary and minimal thinness.
The presentation is largely self-contained and is accessible to graduate students, the only prerequisites being a reasonable grounding in analysis and several variables calculus, and a first course in measure theory. The book will prove an essential reference to all those with an interest in potential theory and its applications.

Keywords

Analysis Complex Analysis Harmonic Functions Poisson integral Potential theory Real Analysis calculus

Authors and affiliations

  • David H. Armitage
    • 1
  • Stephen J. Gardiner
    • 2
  1. 1.Department of Pure MathematicsQueen’s University BelfastBelfastNorthern Ireland
  2. 2.Department of MathematicsUniversity College DublinDublin 4Ireland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-0233-5
  • Copyright Information Springer-Verlag London 2001
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4471-1116-0
  • Online ISBN 978-1-4471-0233-5
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site