Variational Methods in Shape Optimization Problems (Progress in Nonlinear Differential Equations and Their Applications)

From the reviews:

"The book under review deals with some variational methods to treat shape optimization problems ... . The book contains a complete study of mathematical problems for scalar equations and eigenvalues, in particular regarding the existence of solutions in shape optimization. ... The main goal of the book is to focus on the existence of an optimal shape, necessary conditions of optimality, and stability of optimal solutions under some prescribed kind of perturbations." (Jan Sokolowski, Mathematical Reviews, Issue 2006 j)

“The authors predominantly analyze optimal shape and optimal control problems ... . The book, though slim, is rich in content and provides the reader with a wealth of information, numerous analysis and proof techniques, as well as useful references (197 items). ... Numerous nontrivial examples illustrate the theory and can please even those readers who are rather application-oriented.”­­­ (Jan Chleboun, Applications of Mathematics, Vol. 55 (5), 2010)