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On local the representations of $$G$$-closure. (English) Zbl 1123.35320
Summary: We give a representation for the $$G$$-closure of the set of elliptic operators $$H_0^1(W;\mathbb R^m)\to H^1(W;\mathbb R^m)$$ defined by means of the Nemitskii operators where the functions ai are strongly monotone and belong to given sets of uniformly Lipschitz functions, but where the characteristic functions satisfy standard volume restrictions.

##### MSC:
 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 47F05 General theory of partial differential operators
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