**Colloquium Publications**

Volume: 6;
1927;
150 pp;
Softcover

MSC: Primary 30; 31;

Print ISBN: 978-0-8218-4599-8

Product Code: COLL/6

List Price: $39.00

Individual Member Price: $31.20

**Electronic ISBN: 978-1-4704-3156-3
Product Code: COLL/6.E**

List Price: $39.00

Individual Member Price: $31.20

# The Logarithmic Potential: Discontinuous Dirichlet and Neumann Problems

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*Griffith Conrad Evans*

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.

#### Table of Contents

# Table of Contents

## The Logarithmic Potential: Discontinuous Dirichlet and Neumann Problems

- Cover Cover11
- Title page i2
- Dedication iii4
- Preface v6
- Contents vii8
- Preliminary concepts. Stieltjes integrals and Fourier series 110
- Functions harmonic within a circle 2635
- Necessary and sufficient conditions. The Dirichlet problems for the circle 4655
- Potentials of a single layer and the Neumann problem 5564
- General simply connected plane regions and the order of their boundary points 7180
- Plane regions of finite connectivity 8695
- Related problems 121130
- Index 149158
- Back Cover Back Cover1160

#### Readership

Graduate students and research mathematicians interested in differential equations.