Calculus of Variations and Geometric Measure Theory

L. Lussardi - S. Marini - M. Veneroni

Stochastic homogenization of maximal monotone relations and applications

created by lussardi on 01 Mar 2017
modified on 08 Mar 2018


Published Paper

Inserted: 1 mar 2017
Last Updated: 8 mar 2018

Journal: Netw. Heterog. Media
Volume: 13
Number: 1
Pages: 27-45
Year: 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.

Keywords: nonlinear elasticity, stochastic homogenization, random media, Fitzpatrick representation, maximal monotonicity, Ohm-Hall conduction