Variational inequalities and flow in porous media. (English) Zbl 0544.76095

Chipot, M.

Applied Mathematical Sciences, 52. New York etc.: Springer-Verlag. VII, 118 p. DM 44.00; $ 16.10 (1984).

This small lecture note consists of four chapters. It is mainly concerned with the regularity theory for obstacle and dam problems, from the point of view of variational inequalities. The first two chapters summarize some ideas of the functional analysis and the variational inequalities with some applications from physical mathematics. The third chapter is concerned with a regularity theory for the obstacle problem. Results for one and two obstacles are combined in a unified way. The fourth chapter is concerned with the dam problem. There is an excessive use of mathematical symbols many of which could have been avoided for smooth reading. Physical ideas have been over-shadowed by mathematical complexicity, and hence the practical scientists interested in the topic of the flow through porous media will find the book difficult to read. However, a pure mathematician will surely find delight in reading the book.

Reviewer: G.Paria

MSC:

76S05	Flows in porous media; filtration; seepage
35J20	Variational methods for second-order elliptic equations
76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics
49J40	Variational inequalities

Keywords:

Dirichlet problem; penalty method; monotonicity; elastic-plastic torsion; regularity theory for obstacle and dam problems; variational inequalities