On some asymptotical shape problems

Abstract

We consider the problem of the optimal location of a Dirichlet region in a d-dimensional domain Ω subjected to a given force f in order to minimize a given functional. We look for the optimal region among the class of all closed connected sets of assigned total length l. Then we let l tend to infinity and we look at the Γ-limit of a suitable rescaled functional, in order to get information of the asymptotic distribution of the optimal region.