$ G$-CONVERGENCE AND HOMOGENIZATION OF NONLINEAR ELLIPTIC OPERATORS IN DIVERGENCE FORM WITH VARIABLE DOMAIN
Александр Альбертович Ковалевский · Izvestiya Mathematics · 1995
The concepts of -convergence and strong -convergence of a sequence of elliptic operators are studied, where , , are perforated domains contained in a bounded domain . It is established that -convergence of the operators is accompanied by convergence of solutions of certain equations and variational inequalities connected with the operators and a theorem on selection from the sequence of a strongly -convergent subsequence. It is shown that under the condition of periodicity of the perforation of domains and certain assumptions regarding the coefficients of the operators , strong -convergence of to an operator holds with effectively computable coefficients.