Applied Mathematical Sciences

Variational Inequalities and Flow in Porous Media

Authors: Chipot, Michel

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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 case, is one of the most in­ teresting applications of Variational Inequalities with an obstacle. Very little background is needed to read these notes. The main re­ sults of functional analysis which are used here are recalled in the text. The goal of the two first chapters is to introduce the notion of Varia­ tional Inequality and give some applications from physical mathematics. The third chapter is concerned with a regularity theory for the obstacle problems. These problems have now invaded a large domain of applied mathematics including optimal control theory and mechanics, and a collec­ tion of regularity results available seems to be timely. Roughly speaking, for elliptic variational inequalities of second order we prove that the solution has as much regularity as the obstacle(s). We combine here the theory for one or two obstacles in a unified way, and one of our hopes is that the reader will enjoy the wide diversity of techniques used in this approach. The fourth chapter is concerned with the dam problem. This problem has been intensively studied during the past decade (see the books of Baiocchi-Capelo and Kinderlehrer-Stampacchia in the references). The relationship with Variational Inequalities has already been quoted above.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-1-4612-1120-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-0-387-96002-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Variational Inequalities and Flow in Porous Media
Authors
Series Title
Applied Mathematical Sciences
Series Volume
52
Copyright
1984
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1120-4
DOI
10.1007/978-1-4612-1120-4
Softcover ISBN
978-0-387-96002-9
Series ISSN
0066-5452
Edition Number
1
Number of Pages
VII, 118
Topics