In this talk I will present some recent results concerning the stochastic homogenization of a class of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces depending on u. We will show that, under the usual assumptions of stationarity and ergodicity, the homogenization procedure gives rise to a (homogeneous) deterministic free-discontinuity functional belonging to the same class.
Results obtained in collaboration with Filippo Cagnetti (University of Sussex), Gianni Dal Maso (SISSA, Trieste), and Lucia Scardia (University of Bath).