Variational Inequalities and Flow in Porous Media
These notes are the contents of a one semester graduate course which taught at Brown University during the academic year 1981-1982. They are mainly concerned with regularity theory for obstacle problems, and with the dam problem, which, in the rectangular
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Applied Mathematical Sciences EDITORS Fritz John
Courant Institute of MathematicaJ Sciences New York University New York, NY 10012
J.E. Marsden
Department of Mathematics University of California Berkeley, CA 94720
Lawrence Sirovich
Division of Applied Mathematics Brown University Providence, RI 02912
ADVISORS H. Cabannes University of ParifrVI
J. Kelier Stanford University
M. Ghll New York University
G.B. Whltham California Inst. of Technology
J.K. Hale Brown University
EDITORIAL STATEMENT The rnathematization of aII sciences, the fading of traditional scientific boundaries, the impact of computer technology, the growing importance of mathematicalcomputer modelling and the necessity of scientific planning aII create the need both in education and research for books that are introductory to and abreast of these developments. The purpose of this series is to provide such books, suitable for the user of mathematics, the mathematician interested in applications, and the student scientist. In particular, this series will provide an outlet for materialless formally presented and more anticipatory of needs than finished texts or monographs, yet of immediate interest because of the novelty of its treatment of an application or of mathematics being applied or Iying close to applications. The aim of the series is, through rapid publication in an attractive but inexpensive format, to make material of current interest widely accessible. This implies the absence of excessive generality and abstraction, and unrealistic idealization, but with quality of exposition as a goal. Many of the books will originate out of and will stimulate the development of new undergraduate and graduate courses in the applications of mathematics. Some of the books will present introductions to new areas of research, new applications and act as signposts for new directions in the mathematical sciences. This series will often serve as an intermediate stage of the publication of material which, through exposure here, will be further developed and refined. These will appear in conventional format and in hard cover.
MANUSCRIPTS The Editors welcome aII inquiries regarding the submission of manuscripts for the series. Final preparation of aII manuscripts will take place in the editorial offices of the series in the Division of Applied Mathematics, Brown University, Providence, Rhode Island. Springer Science+Business Media, LLC
M. Chipot
Variational Inequalities and Flow in Porous Media
Springer Science+Business Media, LLC
M. Chipot Department of Mathematics University of Nancy 1 B.P. 239-54506 Vandoeuvre Cedex France
AMS Classification: 76805, 49A29
Library of Congress Cataloging in Publication Data Chipot, M. (Michel) Variational inequalities and flow in porous media. (Applied mathematical sciences ; v. 52) Bibliography: p. Includes index. 1. Fluid dynamics. 2. Porous materials. 3. Variational inequalities (Mathematics) 1. Title. II. Series: Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 52. QA1.A647 voI. 52 [QA911]
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