Stochastic homogenization for an integral functional of a quasiconvex function with linear growth

Abstract

We establish the epiconvergence (or Γ-convergence) for the strong topology of L¹(O,R^N) of a sequence of random integral functionals ∫_Of(ω)(x/ε,∇u(x)) dx defined in the space W^1,1(O,R^N). Our method uses an improvement of a convergence result concerning subadditive processes and a recent technique of blow-up combined with the rank one property of the singular measure D^su.