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 …

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 characterize generalized derivatives of the solution operator of the obstacle problem.
This precise characterization requires the usage of the theory of so-called capacitary …

We consider an optimal control problem where the state satisfies a bilateral elliptic
variational inequality and the control functions are the upper and lower obstacles. We seek a …

Abstract 1 Introduction 2 Some classical problems 2.1 The isoperimetric problem 2.2 The
Newton's problem of optimal aerodynamical profiles 2.3 Optimal Dirichlet regions 2.4 …

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 …

We present an abstract framework for irreversible rate independent evolution processes of
quasi-static nature. The main tool relies on the minimizing movement theory. In particular …

In these lecture notes we present a general theory of relaxation for optimal control problems.
The goal is to include into the framework also a class of problems (for instance the ones …

In this paper we consider the quasi-static irreversible evolution of a connected network
related to an average distance functional minimization problem. Our main goal is to extend …

We analyze in this paper the discrete quasi-static irreversible with small steps evolution of a
connected network related to an average distance functional minimization problem. Our …