دانلود کتاب Uniqueness and Non-Uniqueness in the Cauchy Problem

توضیحاتی در مورد کتاب به زبان اصلی :

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