We consider the problem of placing a Dirichlet region made by n small balls of given radius in a given domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look for the Γ−limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of… (More)
We consider an elliptic operator, in divergence form, that is a uniformly elliptic matrix. We describe the behavior of every sequence of domains which minimizes the first Dirichlet eigenvalue over a family of fixed measure domains of R N. The existence of minimizers is proved in some particular situations, for example when the operator is periodic.
We consider an elastic membrane occupying a domain Ω of R N under the action of a given exterior load f. The membrane can be reinforced by the addition of a suitable potential term in the energy; this is usually a boundary term but also other situations can be considered. We study the optimal configuration of the stiffeners which provide the best… (More)