Shape variation and optimization. A geometrical analysis
The book is the English version of the previous French edition, published by Springer [Variation et optimisation de formes. Une analyse géométrique. Berlin: Springer (2005; Zbl 1098.49001)]. In the present version the authors added several new parts and updated the previous ones, so that this new volume consists of 366 pages, with respect to the 334 pages of the previous edition. The purpose of the book remained to present the subject of shape optimization problems in an unified and complete way, from the question of existence of optimal shapes to the analysis of their regularity, without neglecting several interesting examples. The point of view of applications is very deeply considered by the authors, together with the question of efficient numerical schemes to approximate optimal shapes. In this respect, the chapter on shape derivatives has been extended and updated, since it is a crucial step in all numerical approximation algorithms. The book is a very good reference for any scientist who wants to investigate the fascinating field of shape optimization problems. It is also an excellent support for a PhD course; the presence of many exercises, together with many comments and remarks makes the volume a very useful tool for students. For the details on the content of the various chapters we refer to the previous review [Zbl 1098.49001].
scientific article; zbMATH DE number 6838450
scientific article