Problems in Distributions and Partial Differential Equations

C. Zully (Eds.)9780444702487, 0444702482, 9780080872544

The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists. The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader will find many examples of distributions and learn how to work with them. At the beginning of each chapter the relevant theoretical material is briefly recalled. The last chapter is a short introduction to a very wide and important field in analysis which can be considered as the most natural application of distributions, namely the theory of partial differential equations. It includes exercises on the classical differential operators and on fundamental solutions, hypoellipticity, analytic hypoellipticity, Sobolev spaces, local solvability, the Cauchy problem, etc.

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Table of contents :
Content:
Edited by
Page 5

Copyright page
Page 6

Introduction
Page 7

Chapter 1 Preliminaries
Page 11

Basics Chapter 1
Pages 13-24

Chapter 2 The Distributions
Page 25

Basics Chapter 2
Pages 27-50

Chapter 3 Differentiation of Distributions
Page 51

Basics Chapter 3
Pages 53-86

Chapter 4 Convergence of Distributions
Page 87

Basics Chapter 4
Pages 89-109

Chapter 5 Convolution Of Distributions
Page 111

Basics Chapter 5
Pages 113-134

Chapter 6 Fourier and Laplace Transforms of Distributions
Page 135

Basics Chapter 6
Pages 137-181

Chapter 7 Applications
Page 183

Basics Chapter 7
Pages 185-240

Bibliography
Page 241

Index of Words
Pages 243-244

Index of Notations
Page 245