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Random homogenization of an obstacle problem. (English) Zbl 1180.35069
This paper is devoted to the homogenization process of the obstacle problem associated to a perforated domain in the case when the holes are contained in a set of periodically distributed balls of critical size in the sense of [D. Cioranescu and F. Murat, Prog. Nonlinear Differ. Equ. Appl. 31, 45–93 (1997; Zbl 0912.35020)]. While the shape of the holes remains unspecified, the rescaled (with respect to the size of the periodic cell) capacity of every hole is assumed to be given by a stationary ergodic process. In order to prove the convergence result, the authors introduce an auxiliary obstacle problem and appropriately construct a fine corrector.

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
49J40 Variational inequalities
47A35 Ergodic theory of linear operators
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