AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

The Logarithmic Potential: Discontinuous Dirichlet and Neumann Problems
Griffith Conrad Evans
cover
SEARCH THIS BOOK:

Colloquium Publications
1927; 150 pp; softcover
Volume: 6
ISBN-10: 0-8218-4599-3
ISBN-13: 978-0-8218-4599-8
List Price: US$37
Member Price: US$29.60
Order Code: COLL/6
[Add Item]

This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 1924-1925 at the Rice Institute and at the University of Chicago.

Readership

Graduate students and research mathematicians interested in differential equations.

Table of Contents

  • Preliminary concepts. Stieltjes integrals and Fourier series
  • Functions harmonic within a circle
  • Necessary and sufficient conditions. The Dirichlet problems for the circle
  • Potentials of a single layer and the Neumann problem
  • General simply connected plane regions and the order of their boundary points
  • Plane regions of finite connectivity
  • Related problems
  • Index
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia