Special Session 1: ODEs and Applications

Stochastic homogenisation of free-discontinuity problems

Caterina Zeppieri
University of Muenster
Germany
Co-Author(s):    Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia
Abstract:
In this talk I 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 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.