# Book:D.L. Colton/Partial Differential Equations in the Complex Domain

## D.L. Colton: Partial Differential Equations in the Complex Domain

Published $1976$, Pitman Publishing

ISBN 0 273 00101 9.

### Contents

INTRODUCTION
CHAPTER I. PRELIMINARY RESULTS
1. Fundamental Solutions and Analyticity
2. Existence and Uniqueness of Solutions to the Dirichlet and Cauchy Problems
CHAPTER II. IMPROPERLY POSED INITIAL VALUE PROBLEMS
3. Cauchy's Problem in Two Independent Variables
4. Cauchy's Problem for Quasilinear Systems
5. Uniqueness of Solutions to Cauchy's Problem and the Runge Approximation Property
6. The Non-Characteristic Cauchy Problem for Parabolic Equations
7. Improperly Posed Initial-Value Problems for Hyperbolic Equations
CHAPTER III. INTEGRAL OPERATORS FOR ELLIPTIC EQUATIONS
8. Integral Operators in Two Independent Variables
9. Integral Operators for Self Adjoint Equations in Three Independent Variables
10. Integral Operators for Non Self Adjoint Equations in Three Independent Variables
CHAPTER IV. ANALYTIC CONTINUATION
11. Lewy's Reflection Principle and Vekua's Integral Operators
12. The Envelope Method and Analytic Continuation
13. The Axially Symmetric Helmholtz Equation
14. Analytic Continuation of Solutions to the Axially Symmetric Helmholtz Equation
CHAPTER V. PSEUDOPARABOLIC EQUATIONS
15. Pseudoparabolic Equations in One Space Variable
16. Pseudoparabolic Equations in Two Space Variables
REFERENCES