Partial Differential Equations and Calculus of Variations
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and re
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1357 S. Hildebrandt R. Leis (Eds.)
Partial Differential Equations and Calculus of Variations
Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann
1357 S. Hildebrandt R. Leis (Eds.)
Partial Differential Equations and Calculus of Variations
Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors
Stefan Hildebrandt Mathematisches Institut, Universitat Bonn Wegelerstr. 10,5300 Bonn, Federal Republic of Germany Rolf Leis Institut fur Angewandte Mathematik, Universitat Bonn Wegelerstr. 10,5300 Bonn, Federal Republic of Germany
Mathematics Subject Classification (1980): 35A 15 & A30, 35B, 35G, 35J, 35K, 35L, 49F, 53C ISBN 3·540·50508·3 Sprinqer-Verlaq Berlin Heidelberg New York ISBN 0·387·50508·3 Sprinqer-Verlaq New York Berlin Heidelberg
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. 2146/3140-543210
PREFACE This volume contains 18 papers by members and guests of the former Sonderforschungsbereich 72 mierung
years,
in
einer
(SFB 72) "Approximation und Mathematische Opti-
anwendungsbezogenen
who
Mathemat ik",
collaborated in the research group
tialgleichungen und Variationsrechnung".
nave,
over the
partieller Differen-
It is an account of 15 years
of research. The SFB 72 was in existence from 1971 to 1986 as an institute at the university of Bonn. It was supported by the Deutsche Forschungsgemeinschaft,
by the university,
Members
of
the
special
and by the state of NordrheinWestfalen.
research
group
were
mathematicians
holding
chairs at Bonn University as well as younger scientists with temporary positions. They collaborated with colleagues from neighbouring universities and with numerous guests from abroad who visited the SFB 72. In 1986 the SFB 72 reached its maximum life span of 15 years. On this occasion we invited our colleagues and our former guests to contribute a research paper or a survey of a part of our common field of interest, the theory of partial differential equations and the calculus of variations. We hope to have attained a good balance of surveys and of original contributions. The emphasis is on existence and regularity results for variational problems and for nonlinear differential equations,
on
special equations of mathematical physics, and on problems of scattering theory. We would like to take this opportunity to thank all those who have ov
