Stochastic homogenization of subdifferential inclusions via scale integration

Authors

  • Marco Veneroni Fakultat fur Mathematik, TU Dortmund

Abstract

We study the stochastic homogenization of the system

 

 

 

 

σ

η ∈ ∂φη

 

η ∈ ∂φη

 

η ∈ ∂φη

η ∈ ∂φη

div ση = (∇uη),

where

 

 

φη is a sequence of convex stationary random fields, with p-growth. We prove that sequences of solutions (ση, uη) 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.

Downloads