Cartesian Currents in the Calculus of Variations II Variational Inte
Non-scalar variational problems appear in different fields. In geometry, for in stance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in physics, for example in the class
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Volume 38
3. Folge
A Series of Modern Surveys in Mathematics
Editorial Board
E. Bombieri, Princeton S. Feferman, Stanford M. Gromov, Bures-sur-Yvette J. Jost, Leipzig J. Kollar, SaIt Lake City, Utah H.W. Lenstra, Jr., Berkeley P.-L. Lions, Paris R. Remmert (Managing Editor), Munster w. Schmid, Cambridge, Mass. J.Tits, Paris
Springer-Verlag Berlin Heidelberg GmbH
Mariano Giaquinta Giuseppe Modica Jiti Soucek
Cartesian Currents in the Calculus of Variations II Variational Integrals
,
Springer
Mariano Giaquinta Dipartimento di Matematica Universita di Pisa Via F. Buonarroti, 2 1-56127 Pisa Italy Giuseppe Modica Dipartimento di Matematica Applicata Universita di Firenze Via S. Marta, 3 1-50139 Firenze Italy Jiff Soucek Faculty of Mathematics and Physics Charles University Sokolovska,83 18600 Praha 8 Czech Republic
Library of Congress Cata log Ing-In-Pub llcat Ion Data GlaqUlnta. Marlano,
1947Cartes tan currents In the calculus of varlatlons ' MarIano Claqulnta. GIuseppe MOdIca. Jlr; Soucek. p. CIII. -- tErgebnlsse der "'athellatlk und lhrer Grenzgeo1ete
3. FeIge. v. 37-38' Includes bIblIographical references and InDex. ISBN 978-3-662-06218-0 (eBook) ISBN 978-3-642-08375-4 DOI 10.1007/978-3-662-06218-0 2 harl1cover a Ik. paper)
1. Calculus of var-tatlOns. .L. MOdIca. Giuseppe. II. Soucek, Jtr~l. III. Title. IV. Serles: Ergebnisse der Mathe_ank uod lhrer Orenzgeb 1 ete ; 3. Fa 1ge. 8d. 37-38. QA31S.G53 1998 515· .64--dc21
98-18195
CIP
Mathematics Subject Classification (1991): 49Q15, 49Q20, 49Q25, 26B30, 58E20, 73C50, 76A15 ISSN 0071-1136 ISBN 978-3-642-08375-4 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, reuse of illustrations. recitation, broadcasting, reproduction on microfilms or in any other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9. 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the Ger- man Copyright Law. © Springer-Verlag Berlin Heidelberg 1998 Originally published by Springer-Verlag Berlin Heidelberg New York in 1998
Softcover reprint of the hardcover lSt edition 1998
Typesetting: Data conversion by Springer-Verlag 4413111 - 5 4 3 2 1 - Printed on acid-free paper
To Cecilia and Laura, Giulia, Francesca and Sandra, Eva and Sonia.
Preface
Non-scalar variational problems appear in different fields. In geometry, for instance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in physics, for example in the classical theory of a-models. Non linear elasticity is another example in continuum mechanics, while Oseen-Frank theory of liquid crystals and Ginzburg-Landau theory of superconductivity require to treat variational problems in order to model quite comp
