Variational Analysis and Applications
This book discusses a new discipline, variational analysis, which contains the calculus of variations, differential calculus, optimization, and variational inequalities. To such classic branches of mathematics, variational analysis provides a uniform theo
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Nonconvex Optimization and Its Applications V O L U M E 79
Managing Editor: Panos Pardalos
University of Florida, U.S.A. Advisory Board." J. R. Birge
University of Michigan, U.S.A. Ding-Zhu Du
University of Minnesota, U.S.A. C. A. Floudas
Princeton University, U.S.A. J. Mockus
Lithuanian Academy of Sciences, Lithuania H. D. Sherali
Virginia Polytechnic Institute and State University, U.S.A. G. Stavroulakis
Technical University Braunschweig, Germany H. Tuy
National Centre for Natural Science and Technology, Vietnam
V A R I A T I O N A L A N A L Y S I S AND APPLICATIONS
Edited by FRANCO GIANNESSI University of Pisa, Italy ANTONINO MAUGERI University of Catania, Italy
~1 Springer
Library of Congress Cataloging-in-Publication Data A C.I.P. record for this book is available from the Library of Congress.
ISBN-10:0-387-24209-0 e-ISBN-10:0-387-24276-7
ISBN-I_ 3 : 9 7 8 - 0 3 8 7 - 2 4 2 0 9 - 5 e-ISBN-13:978-0387-24276-7
Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 987654321 springeronline.com
SPIN II366270
Contents
Preface
xi PART 1
The Work of G. Stampacchia in Variational Inequalities J.-L. Lions
In Memory of Guido Stampacchia
31
M.G. Garroni
The Collaboration between Guido Stampacchia and Jacques-Louis Lions On Variational Inequalities 33 E. Magenes
In Memory of Guido Stampacchia
39
O. G. Mancino
Guido Stampacchia
47
S. Mazzone
Memories of Guido Stampacchia
79
L. Nirenberg
In Memory of Guido Stampacchia C. Sbordone
81
vi
Variational Analysis and Applications
Guido Stampacchia, My Father G. Stampacchia
83
PART 2 Convergence and Stability of a Regularization Method for Maximal Monotone Inclusions and its Applications to Convex Optimization Ya. L Alber, D. Butnariu and G. Kassay Partitionable Mixed Variational Inequalities E. AllevL A. Gnudi, 1. V. Konnov and E.O. Mazurkevich
89 133
Irreducibility of the Transition Semigroup Associated with the Two Phase Stefan Problem V. Barbu and G. Da Prato
147
On Some Boundary Value Problems for Flows with Shear Dependent Viscosity H. Beir6o da Veiga
161
Homogenization of Systems of Partial Differential Equations A. Bensoussan
173
About the Duality Gap in Vector Optimization G. Bigi and M. Pappalardo
195
Separation of Convex Cones and Extremal Probl
