Stochastic-Periodic Homogenization of Integral Functionals with Convex and Nonstandard Growth Integrands

Abstract: The current investigation aims to study the stochastic-periodic homogenization for a family of functionals with convex and nonstandard growth integrands defined on Orlicz-Sobolev's spaces. It focuses on the concept of stochastic two-scale convergence in this type of spaces, which is a combination of both well-known periodic two-scale convergence and stochastic two-scale convergence in the mean schemes. One fundamental in this topic is to extend the classical compactness results of the stochastic two-scale convergence method to the Orlicz-Sobolev's spaces. Moreover, it is shown, by the stochastic two-scale convergence 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 integrand.