Uniqueness and Non-Uniqueness in the Cauchy Problem

✍ Scribed by Claude Zuily (auth.)

• Publisher: Birkhäuser Basel
• Year: 1983
• Tongue: English
• Leaves: 187
• Series: Progress in Mathematics 33
• Edition: 1
• Category: Library

✦ Synopsis

The study of uniqueness and non-uniqueness is
central to the field of partial differential equations,
and has made considerable progress since its
inception by T. Carleman. The aim of this volume is
to present a survey of many aspects of the theory and
describe the tools used. The expository but high level
treatment introduces the reader to current research;
an exhaustive bibliography is included. This volume
will be valuable as an introduction as well as a
reference book.

CONTENTS

CHAPTER ONE : First order differential operators 1
1 The elliptic case 2
2 The uniqueness theorem under condition (P) 7
3 The non-uniqueness theorem 13
4 The two dimensional case 28
Comments 39

CHAPTER TWO: Calderon's theorem and its extensions 41
1 The case of low multiplicity 41
2 Elliptic operators with non-smooth double characteristics 62
3 The triple complex characteristic case 70
4 A counterexample in higher multiplicity 71
5 Uniqueness theorems in case of higher multiplicity 82
Comments 87

CHAPTER THREE: Uniqueness and pseudo-convexity 89
1 Operators with real principal part 95
2 A class of quasi-homopeneous operators 113
3 The case of double real roots of constant multiplicity 129
4 Elliptic operators 151

Some non-uniqueness results 157

Comments 159

REFERENCES 161

✦ Table of Contents

Front Matter....Pages i-xi
First Order Differential Operators....Pages 1-40
Calderon’s Theorem and Its Extensions....Pages 41-88
Uniqueness and Pseudo-Convexity....Pages 89-160
Back Matter....Pages 161-173

✦ Subjects

Science, general