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Classical Potential Theory

  • Book
  • © 2001

Overview

Authors:
  1. David H. Armitage

    1. Department of Pure Mathematics, Queen’s University Belfast, Belfast, Northern Ireland

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  2. Stephen J. Gardiner

    1. Department of Mathematics, University College Dublin, Dublin 4, Ireland

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    You can also search for this author in PubMed   Google Scholar

  • Written by the world leaders in potential theory
  • Competitive titles are now out of print: an updated introductory text has been long awaited

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Harmonic Functions

    • David H. Armitage, Stephen J. Gardiner
    Pages 1-32

  3. Harmonic Polynomials

    • David H. Armitage, Stephen J. Gardiner
    Pages 33-58

  4. Subharmonic Functions

    • David H. Armitage, Stephen J. Gardiner
    Pages 59-88

  5. Potentials

    • David H. Armitage, Stephen J. Gardiner
    Pages 89-121

  6. Polar Sets and Capacity

    • David H. Armitage, Stephen J. Gardiner
    Pages 123-162

  7. The Dirichlet Problem

    • David H. Armitage, Stephen J. Gardiner
    Pages 163-195

  8. The Fine Topology

    • David H. Armitage, Stephen J. Gardiner
    Pages 197-232

  9. The Martin Boundary

    • David H. Armitage, Stephen J. Gardiner
    Pages 233-272

  10. Boundary Limits

    • David H. Armitage, Stephen J. Gardiner
    Pages 273-304

  11. Back Matter

    Pages 305-333
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Pure Mathematics, Queen’s University Belfast, Belfast, Northern Ireland

    David H. Armitage

  • Department of Mathematics, University College Dublin, Dublin 4, Ireland

    Stephen J. Gardiner

Bibliographic Information

  • Book Title: Classical Potential Theory

  • Authors: David H. Armitage, Stephen J. Gardiner

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4471-0233-5

  • Publisher: Springer London

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 2001

  • Hardcover ISBN: 978-1-85233-618-9Published: 27 October 2000

  • Softcover ISBN: 978-1-4471-1116-0Published: 04 October 2012

  • eBook ISBN: 978-1-4471-0233-5Published: 06 December 2012

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XVI, 333

  • Topics: Functions of a Complex Variable, Analysis, Potential Theory

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