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 tends to infinity and we look at the Γ-limit of a suitable rescaled functional, in order to get information of ...

We determine the asymptotic behaviour of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Γ-convergence arguments. As further developments we consider obstacles with random sizes and shapes located on points of standard lattices, and the case of random homothetics obstacles centered on random Delone sets of points. Obstacle problems for non-local en...

In this paper, a class of minimization problems, labeled by an index 0 < h < 1, is considered. Each minimization problem is for a freeenergy, motivated by the magnetics in 3D-ferromagnetic thin film, and in the context, the index h denotes the thickness of the observing film. The Main Theorem consists of two themes, which are concerned with the study of the solvability (existence of minimizers)...

The behavior of a thin curved hyperelastic film bonded to a fixed substrate is described by an energy composed of a nonlinearly hyperelastic energy term and a debonding interfacial energy term. We compute the Γ-limit of this energy under a noninterpenetration constraint that prohibits penetration of the film into the substrate without excluding contact between them.

We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the problem solution. For the main convergence results of this paper, we use the notion of two-scale convergence. A two-scale homogenized system is obtained as th...

We compute the large-body and the small-particle Gamma-limit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and incompressible materials. In the large-body asymptotics, even if we describe the local orientation of the liquid crystal molecules according to the model of perfect order (Frank ...