The fascinating field of shape optimization problems has received a lot of attention in recent
years, particularly in relation to a number of applications in physics and engineering that …

In this survey paper we present a class of shape optimization problems where the cost
function involves the solution of a PDE of elliptic type in the unknown domain. In particular …

En utilisant l'inégalité de Poincaré et la formule de représentation, on montre que sur le
groupe de Heisenberg de dimension réelle 3, H 1, il existe une constante C> 0 telle que:|∇ …

We study the stability of the solution of a two dimensional elliptic problem with Neumann
boundary conditions, for geometric domain perturbations in the Hausdorff topology. We …

We consider the problem of the optimal location of a Dirichlet region in a two-dimensional
domain Ω subject to a force f in order to minimize the compliance of the configuration. The …

In this paper, we prove the existence of convex classical solutions for a Bernoulli-type free
boundary problem, in the interior of a convex domain. The governing operator considered is …

In this paper, using the Hausdorff topology in the space of open sets under some capacity
constraints on geometrical domains we prove the strong continuity with respect to the …

In this paper, we deal with some shape optimization geometrical inverse spectral problems
involving the first eigenvalue and eigenfunction of ap-Laplace operator, over a class of open …

In this paper we prove a partial C 1, α regularity result in dimension N= 2 for the optimal p-
compliance problem, extending for p≠ 2 some of the results obtained by Chambolle et …

We consider a shape optimization problem written in the optimal control form: the governing
operator is the $ p $-Laplacian in the Euclidean space $\R^ d $, the cost is of an integral …