Stochastic two-scale convergence in the mean in Orlicz-Sobolev's spaces and applications to the homogenization of an integral functional
arXiv:2310.13202 · doi:10.1177/09217134241309718
Abstract
In this paper, 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.
To appear in Asymptotic Analysis journal arXiv admin note: substantial text overlap with arXiv:2311.10103