Stochastic homogenization of subdifferential inclusions via scale integration

Details Stochastic homogenization of subdifferential inclusions via scale integration Stochastic homogenization of subdifferential inclusions via scale integration

2011-07-12

arxiv.org/abs/1107.2374v1

Intl. J. of Struct. Changes in Solids 3 (2011), no. 1, 83-98

Mathematics

Analysis of PDEs

23 pages

Scientific paper

We study the stochastic homogenization of the system -div \sigma^\epsilon = f^\epsilon \sigma^\epsilon \in \partial \phi^\epsilon (\nabla u^\epsilon), where (\phi^\epsilon) is a sequence of convex stationary random fields, with p-growth. We prove that sequences of solutions (\sigma^\epsilon,u^\epsilon) converge to the solutions of a deterministic system having the same subdifferential structure. The proof relies on Birkhoff's ergodic theorem, on the maximal monotonicity of the subdifferential of a convex function, and on a new idea of scale integration, recently introduced by A. Visintin.

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