Nonlinear Analysis and Continuum Mechanics: Papers for the 65th Birthday of James Serrin PDF
Preview Nonlinear Analysis and Continuum Mechanics: Papers for the 65th Birthday of James Serrin
Nonlinear Analysis and Continuum Mechanics Papers for the 65th Birthday of James Serrin Springer New York Berlin Heidelberg Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo Giuseppe Buttazzo Giovanni Paolo Galdi Ermanno Lanconelli Patrizia Pucci Editors Nonlinear Analysis and Continuum Mechanics Papers for the 65th Birthday of James Serrin Springer Giuseppe Buttazzo Giovanni Paolo Galdi Department of Mathematics Department of Engineering University of Pisa University of Ferrara Pisa, 1-56127, Italy Ferrara, 1-44100, Italy Ermanno Lanconelli Patrizia Pucci Department of Mathematics Department of Mathematics University of Bologna University of Perugia Bologna, 1-40126, Italy Perugia, 1-06123, Italy With 3 Figures Library of Congress Cataloging-in-Publication Data Nonlinear analysis and continuum mechanics; papers for the 65th birthday of James Serrin / [editors] Giovanni Paolo Galdi ... let aL]. p. cm. Includes index. ISBN·13:978-1-4612-7455-1 e-ISBN-13:97S-1-4612-2196-S DO I: 10.1007/97S-1-4612-2196-S I. Mathematical analysis. 2. Nonlinear theories. 3. Continuum mechanics. I. Serrin, J. (James), 1926- . II. Galdi, Giovanni P. (Giovanni Paolo), 1947- QA300.5.N663 1997 531' .01 '515355-dc21 97-26098 Printed on acid-free paper. © 1998 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1998 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, 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 known or hereaf ter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Karina Mikhli; manufacturing supervised by Johanna Tschebull. Typeset by BookComp, Inc., Grand Rapids, MI using TeX. 987654321 ISBN-13:978-1-4612-7455-1 Springer-Verlag New York Berlin Heidelberg SPIN 10633994 Contents Foreword vii Contributors ix 1. An Appreciation of James Serrin 1 P.PUCCI 2. On Keplerian N-Body Type Problems 15 A. AMBROSEITI and K. TANAKA 3. Invariance and Balance in Continuum Mechanics 27 G. CAPRIZ and G. MAZZINI 4. Entropy Numbers, Approximation Numbers, and Embeddings 37 D.E. EDMUNDS 5. Some Regularity Properties of Locally Weakly Invertible Maps 45 M. GIAQUlNTA, G. MODICA and J. SOUCEK 6. Some Recent Results on Saint-Venant's Principle 61 R.J. KNOPS and C. LUPOLI 7. Some Results on Modifications of Three-Dimensional Navier-Stokes Equations 73 O.A. LADYZHENSKAYA 8. An Integral Equation in Probability 85 J.B.MCLEOD 9. Self-Similar Solutions of the Second Kind 95 L.A. PELETIER 10. On the Problem of a Moving Contact Angle 107 V.A. SOLONNIKOV 11. Space, Time, and Energy: Lectio Doctoralis 139 J. SERRIN Index 145 Foreword A conference, to celebrate the 65th birthday of Professor James Serrin, was held at the University of Ferrara from 26 to 30 October 1992, on the occasion of the sixth centenary of the foundation of the university. The dual purpose of this conference was to honor James Serrin and to bring together mathematicians in four main areas of Professor Serrin's research in terests: partial differential equations, variational methods, fluid mechanics, and thermodynamics. These fields, with their significant historical connotation, still remain the object of active research and development, and possess a remarkable degree of interrelation in their pure and applied aspects. Thus the organizing committee, consisting of G. Buttazzo, G.P. Galdi, E. Lanconelli, and P. Pucci, had the opportunity to invite a number of well-known mathematicians and friends of James Serrin to make this meeting a success. An honorary committee was also formed, including Professor A. Rossi, Rector of the University of Ferrara, Professor C. Bighi, President of the Accadernia Scienze di Ferrara, Professor G. Del Piero, Decano of the Faculty of Engineering of the University of Ferrara, and Professor L. Zanghirati, Director of the Department of Mathematics of the University of Ferrara. The conference was further supported by G.N.A.F.A., G.N.F.M., and the Mathematics Committee of the Consiglio Nazionale delle Ricerche, together with the University of Ferrara and the Cassa di Risparrnio of Ferrara, to all of whom the organizing committee expresses their most sincere thanks. Many of the lectures delivered at the conference are collected in the present volume, together with several further papers by invited speakers who were unable to attend. The editors cordially thank all these colleagues for their contributions. In addition to the mathematical papers appearing here, there is also included an exposition by P. Pucci concerning aspects of the life of James Serrin and his mathematical work. The second morning of the conference was dedicated to the memory of Professor Lamberto Cesari, a close friend of James Serrin. For this occasion the late Professor Gaetano Fichera delivered a tribute to Lamberto Cesari's remarkable contributions to mathematical analysis. A significant moment of the conference occurred when Professor Serrin was granted the Laurea honoris causa in Ingegneria dei Materiali by the University of Ferrara, presented by the Rector, Professor Antonio Rossi. The Lectio Doctoralis of James Serrin is also included among the contributions. In conclusion, the editors thank Dr. Giovanni Leoni and Dr. Enzo Vitillaro for their valuable assistance in the preparation of this volume. The Editors Contributors Antonio Ambrosetti Scuola Nonnale Superiore, Piazza dei Cavalieri, 7-56126 Pisa, Italy Gianjranco Capriz Dipartimento di Matematica, Universita di Pisa, Via Buonarroti, 2-56127 Pisa, Italy David E. Edmunds School of Mathematics, University of Sussex, Falmer, Brighton BNl 9QH, Sussex, United Kingdom Mariano Giaquinta Dipartimento di Matematica Applicata, Universita di Firenze, Via S. Marta, 3 50139 Firenze, Italy, Robin I. Knops Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, Scot land Olga Ladymenskaya Saint Petersburg Branch of Steklov Institute, Fontanka 27, Saint Petersburg, Russia 191011 C. Lupoli Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, Scot land Giacomo Mazzini Dipartimento di Matematica, Universita di Pisa, Via Buonarroti, 2 56127 Pisa, Italy I. Bryce McLeod Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA Giuseppe Modica Dipartimento di Matematica Applicata, Universita di Firenze, Via S. Marta, 3 50139 Firenze, Italy Lambertus A. Peletier Department of Mathematics, University of Leiden, P.O. Box 9512, 2300R.A. Leiden, The Netherlands x Contributors Patrizia Pucci Dipartimento di Matematica, Universim di Perugia, Via Vanvitelli 1, Perugia, 1- 06123, Italy James Serrin Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA Vsevolod A. Solonnikov Saint Petersburg Branch of Steldov Institute, Fontanka 27, Saint Petersburg, Russia 191011 Jin Soucek Akademie ved Ceske republiky, MatematickY Ustav, Zitmi, 25, 11567 Prima, CR Kazunaga Tanaka Department of Mathemetics, School of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan 1 An Appreciation of James Serrin Patrizia Pucci I am particularly happy to have the opportunity of these proceedings to write a profile of one of my distinguished teachers, with whom I have also had the good fortune to collaborate for so many years, Professor James Serrin. Before entering into my recollection of these years of close association, I would first desire to mention the tribute that Professor Clifford Truesdell wrote in the volume of papers, Analysis and Continuum Mechanics, dedicated to James Serrin on the occasion of his sixtieth birthday, published by Springer-Verlag, in gratitude for his many years of work as coeditor of the Archive for Rational Mechanics and Analysis. The outstanding contributions which Professor Serrin has made, and still makes, to the field of mathematical analysis and its applications are well known. Many of his mathematical discoveries are now in the form of basic principles, whose importance should remain undiminished far into the future. His name is attached to several theorems and methods, and many of his early results have become classical and are well represented in modem textbooks on partial differential equations, calculus of variations, real analysis, fluid mechanics, and thermodynamics: the Gilbarg-Serrin theorem on isolated singularities, the Serrin symmetry theorem, the Meyers-Serrin theorem, the work on quasi-linear elliptic equations, the Ale xandrov-Serrin moving plane technique, the Serrin integral of the calculus of variations, the Peletier-Serrin uniqueness theorem, and the Serrin version of the second law of thermodynamics may be quoted here, as well as other more recent contributions. From this partial list of his most famous results we can also see a further quality of his thought: the aptitude in collaborating with his colleagues and in generously sharing his ideas with them. This aspect of his personality was particularly impressed on me at the conference organized in Minneapolis in May 1991 to celebrate his sixty-fifth birthday, at which a distinguished group of colleagues spoke about his mathematical career. Another distinction of his temperament is the elegance of his taste. This is evi dent in much of his magisterial work, in which each of his theorems has the beauty of an essential form, as in the artistic masterpieces of my country which he loves so much. This is a further reason why his work has influenced others so much, and why many of his theorems have opened new directions in mathematical research. Professor Serrin was born in Chicago on November I, 1926. He first lived in Evanston, where he studied at Evanston Township High School. He then attended G. Buttazzo et al. (eds.), Nonlinear Analysis and Continuum Mechanics © Springer-Verlag New York, Inc. 1998 2 Patrizia Pucci Northwestern University for two years, majoring in Electrical Engineering. After receiving the Bachelor of Arts degree from Western Michigan College, he then went to Indiana University, where in 1951 he received his doctorate with a thesis on the hydrodynamical theory of cavitation, written under the supervision of Professor David Gilbarg. Following his initial appointment as Fine Instructor of Mathematics at Princeton University in 1951, he became C.L.E. Moore Instructor of Mathe matics at the Massachusetts Institute of Technology in the period 1952-1954. In Boston he met and married Barbara West in September 1952, the marvellous and patient partner of his life, who gave him the warmth of a lovely family, gladdened by the birth of three beautiful daughters: Martha, Elizabeth, and Janet. She has shared with him all the anxieties oflife, as well as the recognition which his work receives today. He joined the faculty at the University of Minnesota, as Assistant Professor in Mathematics until 1956, as Associate Professor until 1959, and finally as Professor from then until now. At Minnesota he was named head of the School of Mathematics in the period 1964-1965, and was appointed Regents' Professor of Mathematics in 1969. Professor Serrin has received many honors for his work. He was awarded the degree laurea honoris causa by the University of Sussex in 1972, and by the Universities of Ferrara and Padua in 1992. From the American Mathematical Society he received the George David Birkhoff Award in Applied Mathematics in 1973, and from the Indiana University their Distinguished Alumni Award in 1979. He was elected as a member of the National Academy of Sciences in 1980 and of the American Academy of Arts and Sciences in 1984, and as a fellow of the American Academy for the Advancement of Science in 1980. To commemorate his sixtieth birthday, a series of papers dedicated to him in the Archive for Rational Mechanics and Analysis were collected in the volume Analysis and Continuum Mechanics (Springer-Verlag, 1989), whose dedicatory preface by Professor Clifford Truesdell was already mentioned above. Finally, two conferences were held to celebrate his sixty-fifth birthday: at the University of Minnesota in 1991 and at a corresponding meeting organized by the University of Ferrara in 1992, from which the present volume developed. He has served on numerous professional committees, most recently being Chair of the American Mathematical Society Committee for Progress in Mathematics. He was president of the Society for Natural Philosophy in 1969-1970 and on the council of the American Mathematical Society in 1972-1974. From 1969 to 1986 he was a coeditor of the Archive for Rational Mechanics and Analysis, where his dedicated editorial efforts continued and enhanced its reputation among the great journals of mathematical analysis. He has been on the Editorial Board of the above journal since 1963, and also the Journal ofD ifferential Equations since 1976, the Communications in Partial Differential Equations since 1978, the Rendiconti del Circolo Matematico di Palermo since 1980, the Atti del Seminario Matematico e Fisico dell'Universita di Modena since 1985, Asymptotic Analysis since 1988, and Differential and Integral Equations since 1990.
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