Stochastic homogenization of maximal monotone relations and applications
Luca Lussardi, Stefano Marini, Marco Veneroni · Networks and Heterogeneous Media · 2018
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.