Shape variation and optimization. A geometrical analysis
type: Item
instance of: scholarly article
title: Shape variation and optimization. A geometrical analysis
zbMATH Open document ID: 1392.49001
DOI: 10.4171/178
author: Antoine Henrot
author: Michel Pierre
published in: EMS Tracts in Mathematics
publication date: 2018-02-14T00:00:00Z
review text: 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].
Mathematics Subject Classification ID: 49-02
Mathematics Subject Classification ID: 49Q10
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 49Q12
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 74P20
Mathematics Subject Classification ID: 76M30
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 6838450
zbMATH Keywords: shape optimization
zbMATH Keywords: domain derivation
zbMATH Keywords: eigenvalues
zbMATH Keywords: relaxation
zbMATH Keywords: Gamma-convergence
zbMATH Keywords: homogenization
reviewed by: Giuseppe Buttazzo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/178
OpenAlex ID: W4247473690
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description: scientific article; zbMATH DE number 6838450