Partial Differential Equations and the Calculus of Variations: Essays in Honor of Ennio De Giorgi

503 Pages·1989·37.557 MB·English

by  Jens Frehse (auth.), Ferruccio Colombini, Antonio Marino, Luciano Modica, Sergio Spagnolo (eds.)

Progress in Nonlinear Differential Equations
and Their Applications
Volume 2
Editor
Haim Brezis
Rutgers University
New Brunswick
and
Universitc Pierre et Marie Curie
Paris
Editorial Board
A. Bahri, Rutgers University, New Brunswick
John Ball, Heriot-Watt University
Luis Cafarelli, Institute for Advanced Study
Michael Crandall, University of California, Santa Barbara
Mariano Giaquinta, University of Florence
David Kinderlehrer, University of Minnesota, Minneapolis
Robert Kohn, New York University
P.L. Lions, University of Paris IX
Louis Nirenberg, New York University
Lambertus Peletier, University of Leiden
Paul Rabinowitz, University of Wisconsin, Madison
Partial Differential Equations
and the Calculus
of Variations
Essays in Honor of Ennio De Giorgi
Volume II
Edited by
F. Col om bini
A. Marino
L. Modica
S. Spagnolo
1989 Springer Science+Business Media, LLC
Editare~
Fenuccio Colomhini, Antonio Marino,
Luciano Modica, Sergio Spagnolo
Dipartimenlo di Matematica
Universita di Pisa
Via F. Buonanoti 2
56100 Pisa
ltaly
Library of Congress Cataloging-in-Pttblication Data
Partial diffcrcntial equations and thc calcultJs of variations : essays
in honor of Ennio De Giorgi 1 Ferruccio Colombini ... [et al.].
p. cm. - (Progress in nonlincar differcntial equations and
thcir applications)
l. Diffcrcntial equations, Partial. 2. Calculus of variations.
3. Giorgi, Ennio De. 1. Giorgi, Ennio De. Il. Columbini. F.
(FemJccio) III. Series.
QA377.P297 1989
515' .353-dc20 89-9746
ifJ Springer Science+Business Media New York 1989
Originally published by Birkhăuser Boston in 1989
Softcover reprint ofthe hardcover 1st edition 1989
Ali rights reserved. No part of this publication may be repruducedt stored in a retrieval systcm, or
transmitted, in any form or by any means, electronic, mcchankal, photocopying, recording, or
otherwise, without prior permission of the copyright owner.
Camera-rcady copy preparcd by the editors using TEX.
ISBN 978-1-4615-9833-6 ISBN 978-1-4615-9831-2 (eBook)
DOI 10.1007/978-1-4615-9831-2
A Ennio De Giorgi
i suoi allievi ed amici
con affetto
Courtesy of Foto Fmss~ Pi<a.
Contents
Volume I
Preface vii
A Conversation with Ennio de Giorgi ix
W. K. Allard - An improvement of Carlan's test for
ordinarily . . . 1
F. J. Almgren and M. E. Gurtin A mathematical
contribution to Gibbs's analysis of fluid phases m
equilibrium . . . . . . . . .... 9
H. Attouch and H. Riahi - The epi-continuation method for
minimization problems. Relation with the degree theory
of F.Browder for maximal monotone operators . . . . . . . . . 29
C. Baiocchi Discretization of evolution variational
inequalities . . . . . . . . .... 59
A. Bensoussan - Homogenization for non linear elliptic
equations with random highly oscillatory coefficients . . . . . . 93
L. Boccardo - L00 and L1 variations on a theme of
r -convergence ... 135
H. Brezis and L. Peletier - Asymptotics for elliptic equations
involving critical growth . . . . . . . . . . . 149
G. Buttazzo, G. Dal Maso and U. Mosco Asymptotic
behaviour for Dirichlet problems in domains bounded by
thin layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
viii ContentJ
S. Campanato - Fundamental interior estimates for a class
of second order elliptic operators . . . . . . . . . . . . . . . . . 251
r-
L. Carbone and R. De Arcangelis - Convergence of integral
functionals defined on vector-valued functions . . . . . . . . . 261
M. Carriero, G. Dal Maso, A. Leaci and E. Pascali - Limits
of obstacle problems for the area functional . . . 285
L. Cattabriga - Some remarks on the well-posedness of the
Cauchy problem in Gevrey spaces . . . . . . . . 311
A. Chiffi - Approximating measures and rectifiable curves 321
F. Colombini and S. Spagnolo - A non-uniqueness result for
the operators with principal part a; +a(t )a; . . . . . . . . . . 331
U. D'Ambrosio - A note on duality and the calculus of
variations . . . . ... 355
G. Da Prato - Some results on periodic solutions of
Hamilton-Jacobi equations in Hilbert spaces . . . . . . . 359
Z. Denkowska and Z. Denkowski - Generalized solutions to
ordinary differential equations with discontinuous
right-hand sides via r -convergence ... 371
M. J. Esteban and P. L. Lions - Stationary solutions of
nonlinear Schrodinger equations with an external
magnetic field . . . . . . . . . . . . . . . 401
R. Finn and E. Giusti - On the touching principle 451
W. H. Fleming - Generalized solutions and convex duality in
optimal control . . . . . . . . . . . . . . . . . 461
M. Forti and F. Hansell Models of self-descriptive set
theories ..... .. 473
Contents ix
Volume II
J. Frehse - On a class of nonlinear diagonal elliptic systems
with critical growth and ca.-regularity . . . . . . . . . . .. 519
N. Fusco and C. Sbordone - Higher integrability from reverse
Jensen inequalities with different supports . . . . . . . . . . 541
M. Giaquinta, G. Modica and J. Soucek - Partial regularity
of cartesian currents which minimize certain
variational integrals . . . . . . . . . . . . . . ... 563
G. H. Greco - Thioreme des minimax locaux et fonctions
topologiquement fermees . . . . . . . . . . . . . . 589
R. Hardt and D. Kinderlehrer - Variational principles with
linear growth . . . . . . . . . . . . . . . . . . . . . . 633
H. Kacimi and F. Murat - Estimation de l'erreur dans des
problemes de Dirichlet ou apparait un terme etrange 661
H. Lewy - On atypical variational problems . . . 697
J. L. Lions - Sur la controlabilite exacte elargie . 703
M. Lobo-Hidalgo and E. Sanchez-Palencia - Low and high
frequency vibration in stiff problems . . 729
E. Magenes - A time-discretization scheme approximating
the non-linear evolution equation Ut +ABu= 0 . . . . . . . . 743
P. Marcellini - The stored-energy for some discontinuous
deformations in nonlinear elasticity . . . . . . . . . . . . . . . 767
A. Marino - The calculus of variations and some semilinear
variational inequalities of elliptic and parabolic type . . . 787
S. Mizohata - Some remarks on the dependence domain for
weakly hyperbolic equations with constant multiplicity . . . . . 823
L. Modica - Monotonicity of the energy for entire solutions
of semilinear elliptic equations . . . . . . . . . . . . . . . . . . 843