Problems in Distributions and Partial Differential Equations (eBook)

C. Zuily (Autor)

eBook Download: PDF

1988 | 1. Auflage
240 Seiten
Elsevier Science (Verlag)
978-0-08-087254-4 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Problems in Distributions and Partial Differential Equations 6
Copyright Page 7
INTRODUCTION 8
CONTENTS 10
Chapter 1. Preliminaries 12
Basics 14
Statements of exercises 1 to 8 17
Solutions of exercises 1 to 8 19
Chapter 2. Distributions 26
Basics 28
Statements of exercises 9 to 20 30
Solutions of exercises 9 to 20 34
Chapter 3. Differentiation in the space of distributions 52
Basics 54
Statements of exercises 21 to 41 55
Solutions of exercises 21 to 41 62
Chapter 4. Convergence in the spaces of distributions 88
Basics 90
Statements of exercises 42 to 52 90
Solutions of exercises 42 to 52 95
Chapter 5. Convolution of distributions 112
Basics 114
Statements of exercises 53 to 65 115
Solutions of exercises 53 to 65 119
Chapter 6. Fourier and Laplace transforms of distributions 136
Basics 138
Statements of exercises 66 to 89 142
Solutions of exercises 66 to 89 150
Chapter 7. Applications 184
Statements of exercises 90 to 109 186
Solutions of exercises 90 to 109 202
BIBLIOGRAPHY 242
INDEX 244
INDEX OF NOTATIONS 246

Produkt-Details

• Erscheint lt. Verlag: 1.4.1988
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-087254-9 / 0080872549
• ISBN-13: 978-0-08-087254-4 / 9780080872544