文档介绍：BASIC
LINEAR PARTIAL
DIFFERENTIAL
EQUATIONS
This is a volume in
PURE AND APPLIED MATHEMATICS
A Series of Monographs and Textbooks
Editors: SAMUELEILENBERG AND HYMANBASS
A list of recent titles in this series appears at the end of this volume:
1’1 I’
BASIC
LINEAR PARTIAL
DIFFERENTIAL
EQUATIONS
FranGois Treves
DEPARTMENT OF MATHEMATICS
RUTGERS UNIVERSITY
NEW BRUNSWICK, NEW JERSEY
1975
ACADEMIC PRESS, INC.
(Hartour! Brace lovanovlch, Publishers)
Orlando San Diego San Francisco New York London
Toronto Montreal Sydney Tokyo Sao Paul0
COPYRIGHT0 1975, BY ACADEMICPRESS, INC.
ALL RIGHTS RESERVED.
NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR
TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC
OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY
INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT
PERMISSION IN WRITING FROM THE PUBLISHER.
ACADEMIC PRESS, INC.
Orlando, Florida 32887
United Kingdom Edition published by
ACADEMIC PRESS, INC. (LONDON) LTD.
24/28 Oval Road, London NWl 7DX
Library of Congress Cataloging in Publication Data
Treves, Fransois, (date)
Basic linear partial differential equations.
(Pure and applied mathematics v. 62)
Bibliography: p.
Includes indexes.
1. Differential equations, Partial. 2. Differen-
tial equations, Linear. 1. Title. 11. Series:
Pure and applied mathematics; a series of monographs
and textbooks; v. 62
[QA3741 5 15’.353 74-10206
ISBN 0-12-699440-4
AMS (MOS) 1970 Subject Classifications: 35-02, 35505, 35K05,35L05
PRINTED IN THE UNITED STATES OF AMERICA
838485 987654
Contents
Preface ...ix
Notation xi11
CHAPTER I
The Basic Examples of Linear PDEs
and Their Fundamental Solutions
1. The Basic Examples of Linear PDEs 3
2. Existence and Smoothness of Solutions Not Submitted to Side
Conditions 14
3. Analyticity of Solutions 22
4. Fundamental Solutions of Ordinary Differential E