Abstract
This article deals with the homogenization of the Poisson equation in a bounded domain of , d > 2, which is perforated by a random number of small spherical holes with random radii and positions. We show that for a class of stationary short-range correlated measures for the centres and radii of the holes, we recover in the homogenized limit an averaged analogue of the ‘strange term’ obtained by Cioranescu and Murat in the periodic case [D. Cioranescu and F. Murat, Un term étrange venu d’ailleurs (1986)]. We stress that we only require that the random radii have finite -moment, which is the minimal assumption in order to ensure that the average of the capacity of the balls is finite. Under this assumption, there are holes which overlap with probability one. However, we show that homogenization occurs and that the clustering holes do not have any effect in the resulting homogenized equation.
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