On Compensated Compactness for Nonlinear Elliptic Problems in Perforated Domains

We consider a sequence of Dirichlet problems for a nonlinear divergent operator A: W_m¹(_s) [W_m¹(_s)]^* in a sequence of perforated domains _s . Under a certain condition imposed on the local capacity of the set _s, we prove the following principle of compensated compactness: , where r_s(x) and z_s(x) are sequences weakly convergent in W_m¹() and such that r_s(x) is an analog of a corrector for a homogenization problem and z_s(x) is an arbitrary sequence from whose weak limit is equal to zero.