Calculus of Variations and Geometric Measure Theory
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L. Lussardi - S. Marini - M. Veneroni

Stochastic homogenization of maximal monotone relations and applications

created by lussardi on 01 Mar 2017
modified on 15 Oct 2017


To appear

Inserted: 1 mar 2017
Last Updated: 15 oct 2017

Journal: Netw. Heterog. Media
Pages: 1-22
Year: 2017


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


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