Calculus of Variations and Partial Differential Equations Proceeding
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1340 S. Hildebrandt D. Kinderlehrer M. Miranda (Eds.)
Calculus of Variations and Partial Differential Equations Proceedings of a Conference held in Trento, Italy June 16-21, 1986
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Editors
Stefan Hildebrandt Mathematisches Institut, Universitat Bonn Wegelerstr. 10,5300 Bonn, Federal Republic of Germany David Kinderlehrer School of Mathematics, University of Minnesota 206 Church St. SE, Minneapolis, MN 55455, USA Mario Miranda Centro Internazionale per la Ricerca Matematica 38050 Povo-Trento, Italy
Mathematics Subject Classification (1980): 35A 15, 35G20, 35J20, 35J25, 35J 65,35010 ISBN 3-540-50119-3 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-50119-3 Springer-Verlag New York Berlin Heidelberg
Library of Congress Cataloging-in-Publication Data, Calculus of variations and partial differential equations: proceedings of a conference, held in Trento, Italy, June 16-21, 1986/ S. Hildebrandt, D. Kinderlehrer, M. Miranda, eds. p.crn. - (Lecture notes in mathematics; 1340) Includes bibliographies. ISBN 0-387-50119-3 (U,S,) 1. Calculus of variations - Congresses. 2. Differential equations, Partial- Congresses, I. Hildebrandt, Stefan, II. Kinderlehrer, David. III. Miranda, Mario, 1937-, IV. Series: Lecture notes in mathematics (Springer-Verlag); 1340. 0A3,L28 no. 1340 [OA315] 510 s-dc 19 [515',64] 88-20180 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks, Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1988 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr, 214613140-543210
PREFACE
A delight and a privilege is before us: we have gathered from many nations and across many generations to dedicate this conference and its proceedings to Hans Lewy. The scientific achievements of Professor Lewy are well established. None of us cease to be influenced by the depth and imagination of his scientific vision, by what we may correctly refer to as his genius. Equally important, we have continued to receive our own inspiration from if suo gusto ed il suo garbo - his taste and his style - in his choice of scientific issues and their resolution. His constant dedication to the encouragement of young mathematicians stands before us as a model. We are grateful for this opportunity to demonstrate our esteem and appreciation of Hans Lewy, the man and the scientist.
Stefan Hildebrandt David Kinderlehrer Mario Miranda
Conference Committee
ACKNOWLEDGEMENTS
We wish to thank all the participants for their contribution to the success of the m
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