Inserted: 1 mar 2017
Last Updated: 8 mar 2018
Journal: Netw. Heterog. Media
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.
Keywords: nonlinear elasticity, stochastic homogenization, random media, Fitzpatrick representation, maximal monotonicity, Ohm-Hall conduction