Linear Partial Differential Operators
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MATHEMATISCHEN WISSENSCHAFTEN IN EINZELDARSTELLUNGEN MIT BESONDERER BERUCKSICHTIGUNG DER ANWENDUNGSGEBIETE HERAUSGEGEBEN VON
J. L. DOOB · E. HEINZ · F. HIRZEBRUCH E. HOPF·H.HOPF·W.MAAK · W.MAGNUS F. K. SCHMIDT · K. STEIN GESCHÄFTSFUHRENDE HERAUSGEBER
B.ECKMANN UND B. L.VAN DER WAERDEN ZURICH
BAND 116
Springer-Verlag Berlin Heidelberg GmbH 1964
LINEAR PARTIAL DIFFERENTIAL OPERATORS BY
DR. LARS BORMANDER PROFESSOR AT THE INSTITUTE FOR ADVANCED STUDY PRINCETON, N. J.
SECOND REVISED PRINTING
WITH 1 FIGURE
Springer-Verlag Berlin Heidelberg GmbH
1964
Geschäftsführende Herausgeber: Prof. Dr. B. EcKMANN, Eidgenössische Tecbniscbe Hocbscbule Zürich Prof. Dr. B. L. VAN DER W AERDEN, Mathematisches Institut der Universität Zürich
Alle Rechte, insbesondere das der Übersetzung in fremde Sprachen, vorbehalten Ohne ausdrückliebe Genehmigung des V erlages ist es aucb nicht gestattet, dieses Bucb oder Teile daraus auf photomechanischem Wege (Photokopie, Mikrokopie) oder auf andere Art zu vervielfältigen
© Springer-Verlag Berlin Beideiberg 1963 and 1964 Ursprünglich erschienen bei Springer-Verlag Berlin· Göttingen · Beideiberg 1964 Softcover reprint of the bardeover 2nd edition 1964 ISBN 978-3-662-30654-3 DOI 10.1007/978-3-662-30724-3
ISBN 978-3-662-30724-3 (eBook)
Library of Congress Catalog Card Number 63-12930
Titel-Nr. 5099
LINEAR PARTIAL DIFFERENTIAL OPERATORS BY
DR. LARS BORMANDER PROFESSOR AT THE INSTITUTE FOR ADVANCED STUDY PRINCETON, N. J.
SECOND REVISED PRINTING
WITH 1 FIGURE
1964 Springer-Verlag Berlin Heidelberg GmbH
Library ofCongress Catalog Card Number 63-12930 All rights reserved No part of this book may be reproduced in any form, by microfilm or any other means, without written permissionJrom the publishers
Managing Editors:
Prof. Dr. B, Eckmann, Eirlgnös.risrhe Terhni.rrhe Horb.rrblll1 Ziirirb Prof. Dr. B. L. van der Waerden, Mathematisrhes ln.rlit11t der Universität Ziirirb
Preface The aim of this book is to give a systematic study of questions con~ ceming existence, uniqueness and regularity of solutions of linear partial differential equations and boundary problems. Let us note explicitly that this program does not contain such topics as eigenfunction expan~ sions, although we do give the main facts conceming differential operators which are required for their study. The restriction to linear equations also means that the trouble of achieving minimal assumptions conceming the smoothness of the coefficients of the differential equations studied would not be worth while; we usually assume that they are infinitely differentiable. Functional analysis and distribution theory form the framework for the theory developed here. However, only classical results of functional analysis are used. The terminology employed isthat of BouRBAKI. To make the exposition self-contained we present in Chapter I the elements of distribution theory that are required. With the possible exception of section 1.8, this introductory chapter should be bypassed by a reader who is already familiar with distribution
