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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: Clarendon Press (1984; Zbl 0547.35001)].

MSC:

49J40 Variational inequalities
49-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
35R35 Free boundary problems for PDEs
35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators
35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
74S30 Other numerical methods in solid mechanics (MSC2010)
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
76S05 Flows in porous media; filtration; seepage

Citations:

Zbl 0547.35001