A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Γ-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.

This paper is devoted to prove new relaxation and Γ-convergence theorems on BV(Ω) for a class of integral functionals, whose integrands have a product type structure, but they do not satisfy any assumptions of coerciveness or continuity with respect to the spatial variable.

A variational model for the epitaxial deposition of a film on a rigid substrate in the presence of a crystallographic misfit is studied. The scaling behavior of the minimal energy in terms of the volume of the film and the amplitude of the misfit is considered, and reduced models in the various regimes are derived by Γ-convergence methods. Depending on the relation between the thickness of the ...

This paper is devoted to prove a continuity theorem for integral functional defined on BV(Ω). This result is applied in order to obtain new relaxation and Γ-convergence theorems on BV(Ω) without any coerciveness and any continuity assumption of the integrand with respect to the spatial variable.

this discrete model can be approximated by a continuous energy defined on special functions with bounded variation. In fact, if we limit the interactions in the sum to the nearest neighbors in the portion of εZ contained in some fixed Ω, and we interpret the values ui as the discretization of a function defined in Ω, then these energies can be studied using the methods of Γ-convergence, and the...

We study the asymptotic behavior of functionals associated to the energy of a thin nonlinear elastic spherical shell in the limit of vanishing thickness (proportional to a small parameter) ε and under the assumption of radial deformations. The functionals are characterized by the presence of a nonlocal potential term and defined on suitable weighted functional spaces. The transition shell-membr...

In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only approximates well the area functional up to the first order. However, as an application of our result, we prove, assuming the singlemultiplicity property of the limiting energy, that the Morse indic...