Stochastic Two-Scale Convergence in the Mean in Orlicz-Sobolev’s Spaces and Applications to the Homogenization of an Integral Functional

In this article, we study the stochastic homogenization for a family of integral functionals with convex and nonstandard growth integrands defined on Orlicz-Sobolev’s spaces. One fundamental in this topic is to extend the classical compactness results of the two-scale convergence in the mean method to this type of spaces. Moreover, it is shown by the two-scale convergence in the mean method that the sequence of minimizers of a class of highly oscillatory minimizations problems involving convex functionals converges to the minimizers of a homogenized problem with a suitable convex function. 1