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Variational and quasivariational inequalities. Applications to free boundary problems. Transl. from the Italian by Lakshmi Jayakar. (English) Zbl 0551.49007
A Wiley-Interscience Publication. Chichester etc.: John Wiley and Sons. IX, 452 p. £ 29.50 (1984).
This book provides a self-contained treatment of variational and quasi variational inequalities theory which provides a unified and general formulation of a wide class of unilateral and free boundary problems arising in elasticity, fluid flow through porous media, economics and transportation equilibrium etc. Written by one of the pioneers, C. Baiocchi, the book contains enough material for engineers and mathematicians alike. Indeed, the book is very well written and presented and is a useful source for professionals working in the engineering and mathematical sciences. This book equips the reader with an overall logic of formulating and successfully studying the many unrelated moving and free boundary value problems in the framework of variational inequality theory. For the numerical treatment of variational inequalities, see an excellent book by J. Crank [Free and moving boundary problems, Oxford (1984)].
Reviewer: M.A.Noor

49J40Variational methods including variational inequalities
49-01Textbooks (calculus of variations)
35R35Free boundary problems for PDE
35J85Unilateral problems; variational inequalities (elliptic type) (MSC2000)
35K85Linear parabolic unilateral problems; linear parabolic variational inequalities
74S30Other numerical methods in solid mechanics
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
76S05Flows in porous media; filtration; seepage