Abstract

This talk is concerned with the asymptotic analysis via $\Gamma$-convergence of energy-driven discrete systems when the lattice spacing vanishes. We focus on a class of energy functionals for which the energy densities contain both a bulk and a surface scaling. In the discrete-to-continuum limit such energy functionals typically converge to free-discontinuity functionals, which have natural applications in image segmentation and fracture mechanics.

After presenting some prototypical examples I will discuss a recent result obtained in collaboration with Andrea Braides and Marco Cicalese, where we consider a very general class of discrete energies giving rise to a free-discontinuity functional in the $\Gamma$-limit.