Obstacle problems in mathematical physics. (English) Zbl 0606.73017

Rodrigues, José-Francisco

North-Holland Mathematics Studies, 134, Notas de Matemática (114). Amsterdam etc.: North-Holland. XV, 352 p. $ 71.00; Dfl. 160.00 (1987).

This volume presents a general account of the applicability of elliptic variational inequalities (VI) to free boundary problems of obstacle type in the context of classical applied mathematics.
The book is divided into three parts. The first is a presentation of some obstacle type problems which can be reduced to VI. The second part discusses some of the main aspects of the theory of elliptic VI in abstract Hilbert space framework, properties of the free boundary and some results on the obstacle Plateau problem. Finally, applications to various free boundary problems, including lubrication-cavitation, elastoplastic, boundary obstacle, dam, continuous casting, electromachining, and flow with wake problems are detailed.
As prerequisite some elements of functional analysis and of second order elliptic partial differential equations are needed. A large bibliography rounds out the volume.

Reviewer: W.Ames

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
49J40	Variational inequalities
35R35	Free boundary problems for PDEs
35J85	Unilateral problems; variational inequalities (elliptic type) (MSC2000)
74-02	Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids

Keywords:

elliptic variational inequalities; obstacle type problems; abstract Hilbert space framework; obstacle Plateau problem; lubrication- cavitation; elastoplastic; boundary obstacle; dam; continuous casting; electromachining; second order elliptic partial differential equations