Random homogenization of an obstacle problem
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 [\textit{D. Cioranescu} and \textit{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.
scientific article; zbMATH DE number 5544192