Ce livre est une initiation aux approches modernes de l’optimisation mathématique de formes. Il s’appuie sur les seules connaissances de première année de Master de mathématiques, mais permet déjà d’aborder les questions ouvertes dans ce domaine en pleine effervescence. On y développe la méthodologie ainsi que les outils d’analyse mathématique et de géométrie nécessaires à l’étude des variations de domaines. On y trouve une étude systématique des questions géométriques associées à l’opérateur de Laplace, de la capacité classique, de la dérivation par rapport à une forme, ainsi qu’un FAQ sur les topologies usuelles sur les domaines et sur les propriétés géométriques des formes optimales avec ce qui se passe quand elles n’existent pas, le tout avec une importante bibliographie.
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From the reviews:
"The book under review is devoted to the very interesting field of shape optimization problems, which received a lot of attention in the recent years. ... many examples coming from applications are presented. The book also includes many exercises which, together with all the remarks, comments and presentations of problems still open, make the volume an excellent choice for anyone who wants to approach the fascinating field of shape optimization." (Giuseppe Buttazo, Zentralblatt MATH, Vol. 1098 (24), 2006)
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