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...