Geodesic
Homogenization of non-linear second-order elliptic equations in perforated domains
Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 69-88

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The classical homogenization method of elliptic boundary value problems is based on the continuation of a solution, given in a perforated domain, to the entire initial domain. This method requires substantial restrictions on the perforated domain (the “strong connectedness” condition). In this paper we propose a new approach, which does not use the continuation technique. Here the “strong connectedness” is replaced by the usual connectedness. 
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     author = {V. V. Zhikov and M. E. Rychago},
     title = {Homogenization of non-linear second-order elliptic equations in perforated domains},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a2/}
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V. V. Zhikov; M. E. Rychago. Homogenization of non-linear second-order elliptic equations in perforated domains. Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 69-88. http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a2/