The Analysis of Linear Partial Differential Operators I Distribution
In 1963 my book entitled "Linear partial differential operators" was published in the Grundlehren series. Some parts of it have aged well but others have been made obsolete for quite some time by techniques using pseudo-differential and Fourier integral o
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Editors M. Artin S.S. Chern J.L. Doob A. Grothendieck E. Heinz F. Hirzebruch L. H6rmander S.MacLane WMagnus C.C.Moore IK.Moser M.Nagata WSchmidt D.S.Scott ITits RL. van der Waerden Managing Editors M. Berger R Eckmann S.R.S. Varadhan
Lars Hormander
The Analysis of Linear Partial Differential Operators I Distribution Theory and Fourier Analysis
Springer-Verlag Berlin Heidelberg NewYork Tokyo 1983
J. David Logan Department of Mathematics and Statistics University of Nebraska at Lincoln Lincoln, NE 68588-0323 USA Editorial Board
S. Axler Mathematics Department San Francisco State University San Francisco, CA 94132 USA
F.W. Gehring Mathematics Department East Hall University of Michigan Ann Arbor, MI 48109 USA
K.A. Ribet
Department of Mathematics University of California at Berkeley Berkeley, CA 94720-3840 USA
Mathematics Subject Classification (1991): 35-01
Library of Congress Cataloging-in-Publication Data Logan, J. David (John David) Applied partial differential equations / J. David Logan. p. cm.-(Undergraduate texts in mathematics) Includes bibliographical references and index. ISBN·I3: 978·3·642·96752·8 .·ISBN·I3: 978·3·642·96750·4 DOl: 10.1007/978·3·642·96750-4
1. Differential equations, Partial. QA377.L578 1998 515'.353-dc21
I. Title.
II. Series. 97-48861
Printed on acid-free paper.
© 1998 Springer-Verlag New York, Inc.
Softcover reprint of the hardcover 1st edition 1998 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, . as understood by the 1l:ade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Victoria Evarretta; manufacturing supervised by Jacqui Ashri. Photocomposed copy prepared from the author's files by The Bartlett Press, Inc.
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Preface
In 1963 my book entitled "Linear partial differential operators" was published in the Grundlehren series. Some parts of it have aged well but others have been made obsolete for quite some time by techniques using pseudo-differential and Fourier integral operators. The rapid development has made it difficult to bring the book up to date. However, the new methods seem to have matured enough now to make an attempt worth while. The progress in the theory of linear partial differential equations during the past 30 years owes much to the theory of distributions created by Laurent Schwartz at the end of the 1940's. It summed up a great deal of the experience
