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Stochastic homogenization of maximal monotone relations and applications

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  • 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.

    Mathematics Subject Classification: Primary: 35B27, 47H05, 49J40; Secondary: 74B20, 74Q15, 78M40.

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