Stochastic homogenization of maximal monotone relations and applications

Luca Lussardi, Stefano Marini, Marco Veneroni

Published 2017-02-27Version 1

We study the homogenization of a stationary random maximal monotone operator on a probability space equipped with an ergodic dynamical system. The proof relies on Fitzpatrick's variational formulation of monotone relations, on Visintin's scale integration/disintegration theory and on Tartar-Murat's compensated compactness. We provide applications to systems of PDEs with random coefficients arising in electromagnetism and in nonlinear elasticity.