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Book review

Author(s) Sokolowski, Jan
Zolesio, Jean-Paul
Title Introduction to shape optimization
Publisher Springer-Verlag
Year of publication 1992
Reviewed by Ioan A. Rus

This monograph deals with the shape sensitivity analysis. It is organized in four chapters. In the first the basic notions, such as the material derivative and the shape derivative of domain functionals, are presented. The second is concerned with mathematical methods used in the shape sensitivity analysis (shape functionals for problems governed by partial differential equations, speed method, material derivatives, shape derivatives, ...). The third is about shape derivative for linear problems. The sections of this chapter are the following: The shape derivative for the Dirichlet boundary value problem, The shape derivative for the Neumann boundary value problem, Necessary optimality conditions, Parabolic equations, Neumann boundary conditions, Dirichlet boundary conditions, Shape sensitivity in elasticity, Shape sensitivity analysis of the smallest eigenvalue, shape sensitivity analysis of Kirchhoff plate, Shape derivatives of boundary integrals, shape sensitivity analysis of boundary value problems with singularities. The fourth chapter is concerned with the shape sensitivity analysis of variational inequalities.

This book is written as a research monograph on Shape optimization. I recommend it to all who are interested in Partial differential equations, Optimization theory and Mechanics of solids.