Homogenisation and θ — 2 convergence

Abstract

We introduce a new concept of convergence for bounded sequences of functions in L2(Ω), called θ – 2 convergence, where Ω is an open set of ℝn and θ a C2 diffeomorphism of ℝn. This tool enables us to deal with homogenisation problems in some nonperiodic perforated domains. In particular, it provides a simple proof, and extensions, of a recent result of M. Briane.