Partial Differential Equations
The book has been completely rewritten for this new edition. While most of the material found in the earlier editions has been retained, though in changed form, there are considerable additions, in which extensive use is made of Fourier transform techniqu
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Fritz John
Partial Differential Equations Third Edition
Springer-Verlag
New York· Heidelberg· Berlin
Fritz John Courant Institute of Mathematical Sciences New York University New York, NY 10012 USA
Editors
Fritz John
Lawrence Sirovich
Courant Institute of Mathematical Sciences New York University New York, NY 10012 USA
Division of Applied Mathematics Brown University Providence, RI 02912 USA
Joseph P. LaSalle
Gerald B. Whitham
Division of Applied Mathematics Brown University Providence, RI 02912 USA
Applied Mathematics Firestone Laboratory California Institute of Technology Pasadena, CA 91125 USA
AMS Subject Classifications: 35-02, 35AIO, 35EXX, 35L05, 35LlO
Library of Congress Cataloging in Publication Data John, Fritz 1910Partial differential equations. (Applied mathematical sciences; v. I) Bibliography: p. Includes index. I. Differential equations, Partial. I. Title. II. Series. QAl.A647 vol. I 1978 [QA374] 510'.8s [515'.353] 78-10449
All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag. Copyright © 1971, 1975, 1978 by Springer-Verlag New York Inc. Softcover reprint ofthe hardcover 3rd edition 1978
ISBN -13: 978-1-4684-0061-8 DOl: 10.1007/978-1-4684-0059-5
e-ISBN -13: 978-1-4684-0059-5
Preface to the Third Edition
The book has been completely rewritten for this new edition. While most of the material found in the earlier editions has been retained, though in changed form, there are considerable additions, in which extensive use is made of Fourier transform techniques, Hilbert space, and finite difference methods. A condensed version of the present work was presented in a series of lectures as part of the Tata Institute of Fundamental Research -Indian Institute of Science Mathematics Programme in Bangalore in 1977. I am indebted to Professor K. G. Ramanathan for the opportunity to participate in this exciting educational venture, and to Professor K. Balagangadharan for his ever ready help and advice and many stimulating discussions. Very special thanks are due to N. Sivaramakrishnan and R. Mythili, who ably and cheerfully prepared notes of my lectures which I was able to use as the nucleus of the present edition. A word about the choice of material. The constraints imposed by a partial differential equation on its solutions (like those imposed by the environment on a living organism) have an infinite variety of consequences, local and global, identities and inequalities. Theories of such equations usually attempt to analyse the structure of individual solutions and of the whole manifold of solutions by testing the compatibility of the differential equation with various types of additional constraints. The problems arising in this way have challenged the ingenuity of mathematicians for centuries. It is good to keep in mind that there is no single "central" problem; new applications ·commonly lead to new questions never envisioned before. In this book emphasis is put on discovering significant features of a diffe
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