Two Scale Convergence

Abstract : Many information like oscillations contained in a sequence is lost in the limit under weak convergence. This lost information is very crucial in applications especially in the study composite materials and hence in homogenization. In this talk, we introduce relatively a new notion of convergence, namely two-scale convergence, more generally multi-scale convergence through which we recover some lost information. We will establish a compactness theorem in two-scale convergence and indicate its application to homogenization. If time permits, we also introduce a more general notion, namely the method of unfolding.