Stochastic homogenization of subdifferential inclusions via scale integration
Marco Veneroni · Technische Universität Dortmund Eldorado (Technische Universität Dortmund) · 2010
We study the stochastic homogenization of the system − σ η ∈ ∂φ η η ∈ ∂φ η η ∈ ∂φ η η ∈ ∂φ η div σ η = f η ( ∇ u η ) , where φ η is a sequence of convex stationary random fields, with p -growth. We prove that sequences of solutions ( σ η , u η ) 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.