Stochastic homogenization of subdifferential inclusions via scale integration

Abstract

We study the stochastic homogenization of the system -div σ^ε= f^εσ^ε\in \partial ϕ^ε(\nabla u^ε), where (ϕ^ε) is a sequence of convex stationary random fields, with p-growth. We prove that sequences of solutions (σ^ε,u^ε) converge to the solutions of a deterministic system having the same subdifferential structure. The proof relies on Birkhoff's ergodic theorem, on the maximal monotonicity of the subdifferential of a convex function, and on a new idea of scale integration, recently introduced by A. Visintin.

23 pages