Reiterated $\Sigma$-Convergence In Orlicz Setting and Applications

Abstract

The concept of reiterated $\Sigma$-convergence (and more generally of multiscale $\Sigma$-convergence) is extended to framework of Orlicz-Sobolev spaces, in order to deals with homogenization of multiscales problems in general deterministic setting and whose solutions leads in this type of spaces. This concept relies on the notion of reiterated homogenization supralgebra that we will assumed being ergodic. An application to the deterministic reiterated homogenization of nonlinear degenerate elliptic operators with nonstandard growth is given and some concrete homogenization problems following varied structure hypothesis are deduce from this latter.