Non-Homogeneous Boundary Value Problems and Applications Volume III
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llerausgegeben von ]. L. Doob . A. Grothendieck . E. Heinz . F. Hirzebruch E. Hopf . W. Maak . S. MacLane . W. Magnus .]. K. Moser M. M. Postnikov . F. K. Schmidt . D. S. Scott . K. Stein
Geschäftsführende Herausgeber B. Eckmann und B. 1. van der Waerden
J.L.Lions. E.Magenes
Non -Homogeneous Boundary Value Problems and Applications Translated from the French by P. Kenneth
Volume III
Springer-Verlag Berlin Heidelberg New Y ork 1973
J. L. Lions . E. Magenes
Non -Homogeneous Boundary Value Problems and Applications Translated from the French by P.Kenneth
Volume III
Springer-Verlag NewYork Heide1berg Berlin 1973
J.L. Lions
E.Magenes
University of Paris
University of Pavia
TitIe of the French Original Edition: Problemes aux limites non homogenes et applications (tome II!) Publisher: S. A. Dunod, Paris 1968
Transla tor:
P. Kenneth Paris
Geschäftsführende Herausgeber:
B. Eckmann Eidgenössische Technische Hochschule Zürich
B. L. van der Waerden Mathematisches Institut der Universität Zürich
AMS Subject Classifications (1970) Primary
35J20, 35J25, 35J30, 35J35, 35J40, 35K20, 35K35, 35L20, Secondary 46E35, 46F15, 46F99
ISBN-13:978-3-642-65395-7
e-ISBN-13:978-3-642-65393-3
DOI: 10.1007/978-3-642-65393-3 This \york is subject to copyright. All rights are reserved, whether the whole cr part of thc material 1S conccrned, specifically those of translation) reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine Of similar means, and storage in data banks. Undcr § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. by Springer-Verlag, Berlin . Heidelberg 1973.Softcover reprint of the hardcover 1st edition 1973 Library of Congress Catalog Card Number 71-151407
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Preface to the English Translation The present translation follows the French edition without change, except for some corrections which were suggested to us by the remarks of C. Baiocchi and M. L. Bernardi, to whom we express our sincerest thanks. We have added a complementary bibliography. We also wish to thank P. Kenneth for his excellent work of translation. Paris/Pavia, March 1972
J. L. LIONS
E. MAGENES
Introduction 1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN,
(2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1 < f < v, where Pis a linear differential operator in mand where the Q/s are linear differential operators on am. In Volumes 1 and 2, we studied, for particular c1asses of systems {P, Qj}, problem (1), (2) in c1asses of Sobolev spaces (in general constructed starting from P) of positive integer or (by interpolation) non-integer order; then, by transposition, in c1asses of Sobolev spaces of negative order, until, by passage to the limit on the order, we reached the spaces of distributions of finite order. In this volume, we study the analogous problems in spaces of inlinit
