Abstract
We propose an abstract framework for the homogenization of random functionals which may contain non-convex terms, based on a two-scale Γ -convergence approach and a definition of Young measures on micropatterns which encodes the profiles of the oscillating functions and of functionals. Our abstract result is a lower bound for such energies in terms of a cell problem (on large expanding cells) and the Γ -limits of the functionals at the microscale. We show that our method allows to retrieve the results of Dal Maso and Modica in the well-known case of the stochastic homogenization of convex Lagrangians. As an application, we also show how our method allows to stochastically homogenize a variational problem introduced and studied by Alberti and Müller, which is a paradigm of a problem where an additional mesoscale arises naturally due to the non-convexity of the singular perturbation (lower order) terms in the functional.
Original language | English (US) |
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Article number | 156 |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 56 |
Issue number | 6 |
DOIs | |
State | Published - Dec 1 2017 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics