TU Dortmund, Raum M611

In this talk we introduce a general class of singularly-perturbed elliptic functionals Fε and we study their asymptotic behaviour as the perturbation parameter ε > 0 vanishes. Under suitable assumptions, which in particular allow us to bound Fε by the Ambrosio-Tortorelli functionals, we show that the functionals Fε Γ-converge to a free-discontinuity functional of brittle type. This is a consequence of a volume-surface decoupling effect. If time permits, in the last part we will discuss the application of the general convergence result to the setting of stochastic homogenization. This result was obtained in collaboration with Annika Bach & Caterina Ida Zeppieri.

Roberta Marziani