Calculus of Variations II
This long-awaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometri
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Series editors A. Chenciner S.S. Chern B. Eckmann P. de la Harpe F. Hirzebruch N. Hitchin 1. Hörmander M.-A. Knus A. Kupiainen G. Lebeau M. Ratner D. Serre Y.G. Sinai N.J.A. Sloane J. Tits B. Totaro A. Vershik M. Waldschmidt
Editor-in-Chief M. Berger
J.Coates
S.R.S. Varadhan
311
Springer-Verlag Berlin Heidelberg GmbH
Mariano Giaquinta Stefan Hildebrandt
Calculus of Variations 11 With 82 Figures
,
Springer
Mariano Giaquinta
Stefan Hildebrandt
Scuola Normale Superiore Piazza dei Cavalieri, 7 56lO0 Pisa, Italy
Universität Bonn Mathematisches Institut Wegelerstr. lO 53115 Bonn, Germany
1st ed. 1996. Corr. 2nd printing 2004
Iibrary ofCongress Cataloging-in-Publication Data. Giaquinta, Mariano, 1947- .Calculus of variations/Mariano Giaquinta, Stefan Hildebrandt. p. cm.-(Grundlehren der mathematischen Wissenschaften; 310-311) Includes bibliographical references and indexes. Contents: 1. The Lagrangian formalism-2. The Hamiltonian formalism. ISBN 978-3-642-08192-7 ISBN 978-3-662-06201-2 (eBook) DOI 10.1007/978-3-662-06201-2 1. Calculus of variations I. Hildebrandt, Stefan. II. Title. III. Series. QA315.G46 1996 515'.64-dc20 96-20429
Mathematics Subject Classification: 49-XX, 53-XX, 70-XXl
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© Springer-Verlag Berlin Heidelberg 2004
Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover ISt edition 2004
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Preface
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the formal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as weIl as HamiltonJacobi theory and the classical theory of partial differential equations of first order. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often n
