**Translations of Mathematical Monographs**

1992;
303 pp;
Hardcover

MSC: Primary 30; 47;
Secondary 81

Print ISBN: 978-0-8218-4562-2

Product Code: MMONO/106

List Price: $122.00

AMS Member Price: $97.60

MAA Member Price: $109.80

**Electronic ISBN: 978-1-4704-4517-1
Product Code: MMONO/106.E**

List Price: $122.00

AMS Member Price: $97.60

MAA Member Price: $109.80

# Conformal Mappings and Boundary Value Problems

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*Guo-Chun Wen*

This book presents a systematic exposition of the theory
of conformal mappings, boundary value problems for analytic and
harmonic functions, and the relationship between the two subjects. It
is suitable for use as an undergraduate or graduate level textbook,
and exercises are included.

The first three chapters recount existence and uniqueness theorems of
conformal mappings from simply and multiply connected domains
to standard domains, some properties of analytic functions,
harmonic functions and schlicht meromorphic functions, and
representations of conformal mappings. In the remaining three chapters,
the basic boundary value problems for analytic and harmonic functions
are discussed in detail, including some new methods and results
obtained by the author. For example, the Riemann-Hilbert boundary value
problem with piecewise continuous coefficients in a multiply connected
domain is covered in chapter five, and some irregular oblique
derivative problems are treated in chapter six.

#### Readership

Graduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis.

#### Reviews & Endorsements

The exposition is clear and very detailed … most constructive methods are described in detail while in the proofs of theorems every step is made explicitly. Moreover at the end of each chapter a series of exercises is provided, allowing the reader to check his/her understanding of the preceeding chapter.

-- mededelingen van het wiskundig genootschap

Suitable for use as an undergraduate or graduate level textbook.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Conformal Mappings and Boundary Value Problems

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Chapter 1. Some properties of analytic and harmonic functions 110
- Chapter 2. Conformal mappings of simply connected domains 2534
- Chapter 3. Conformal mappings of multiply connected domains 95104
- Chapter 4. Applications of integrals of Cauchy type to boundary value problems 137146
- Chapter 5. The Hilbert boundary value problem for analytic functions on multiply connected domains 189198
- Chapter 6. Basic boundary value problems for harmonic functions 231240
- Appendix 1. A brief introduction to quasiconformal mappings 273282
- Appendix 2. Some connections between integral equations and boundary value problems 285294
- References 299308
- Subject Index 301310
- Back Cover Back Cover1314