The energy of a Von Kármán circular plate is described by a nonlocal nonconvex one-dimensional functional depending on the thickness ε. Here we perform the asymptotic analysis via Γ-convergence as the parameter ε goes to zero.

We show the Γ-convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional. The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the edges of the segmentation is replaced by a nonconvex functional.

The formation of microdomains, also called rafts, in biomembranes can be attributed to the surface tension of the membrane. In order to model this phenomenon, a model involving a coupling between the local composition and the local curvature was proposed by Seul and Andelman in 1995. In addition to the familiar Cahn-Hilliard/Modica-Mortola energy, there are additional ‘forces’ that prevent larg...

In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter ε, representing the interface thickness between the tumorous and non tumorous cells, tends to zero. More in particular, we analyze here a gradient-flow type model arising from a modification of the recently introduced model for tumor growth dynamics in...

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...