Convergence of monotone operators with respect to measures

Abstract

This paper deals with monotone operators in the theory of homogenization. The operators introduced may depend on a small parameter δ. We establish some convergence results with respect to singular measures. Our result is valid without using the two-scale convergence. A comparison between the operators for the singular structure and the classical ones is obtained when the thickness δ of the structure vanishes. Finally, under some suitable assumptions, we show the commutativity of the corresponding diagram.