Deterministic homogenization of nonlinear degenerate elliptic operators with nonstandard growth

We study the deterministic homogenization of nonlinear degenerate elliptic equations with nonstandard growth. One fundamental in this topic is to extend the classical compactness results of the Σ-convergence method to the Orlicz spaces. We also show that one can homogenize nonlinear Dirichlet problems in a general way by leaning on a simple abstract hypothesis contrary to what has been done in the determinstic homogenization theory.