Variational Inequalities and Flow in Porous Media

M. Chipot (Autor)

Buch | Softcover

118 Seiten

1984 | Softcover reprint of the original 1st ed. 1984
Springer-Verlag New York Inc.
978-0-387-96002-9 (ISBN)

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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.

1. Abstract Existence and Uniqueness Results for Solutions of Variational Inequalities.- 2. Examples and Applications.- 3. The Obstacle Problems: A Regularity Theory.- 4. The Dam Problem.- References.

Erscheint lt. Verlag	1.6.1984
Reihe/Serie	Applied Mathematical Sciences ; 52
Zusatzinfo	VII, 118 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Technik ► Maschinenbau
ISBN-10	0-387-96002-3 / 0387960023
ISBN-13	978-0-387-96002-9 / 9780387960029
Zustand	Neuware