We study a dissimilarity measure between shapes, expressed by the natural pseudodistance between size pairs, where a shape is viewed as a topological space endowed with a real-valued continuous function. Measuring dissimilarity amounts to minimizing the change in the functions due to the application of homeomorphisms between topological spaces, with respect to the L∞-norm. A new class of shape ...

This work is a survey on optimal control methods applied to shape optimization problems. The unknown character of the domain where the state system is defined creates major difficulties both for the theoretical analysis and for the implementation of the numerical approximation methods. The optimal control and the controllability methods for elliptic equations allow the development of approximat...