Mathematical challenges in shape optimization

Antoine Henrot (1, 2) , Jan Sokolowski (1)

1 IECN - Institut Élie Cartan de Nancy
2 CORIDA - Robust control of infinite dimensional systems and applications

This paper covers some theoretical investigations performed in France, in the framework of the CNRS programme GDR {\it Applications Nouvelles de l'Optimisation de Forme}. The programme included also some activities in Poland. We do not restrict the presentation to the French community in the research field, the list of references includes all recent monographs on the shape optimization. The outline of the paper is the following. First we present some main fields of the activity in shape optimization. To present some precise results, from mathematical point of view, we include two sections. The first is devoted to the eigenvalues, the second to the drag minimization. Many theoretical questions related to these problems are still open.

Domaines: Equations aux dérivées partielles [math.AP]

Antoine Henrot, Jan Sokolowski. Mathematical challenges in shape optimization. Control and Cybernetics, 2005, 34, numéro 1, pp.37-57. ⟨hal-00092356⟩