Modification of unfolding approach to two-scale convergence

Abstract

Two-scale convergence is a powerful mathematical tool in periodic homogeniza- tion developed for modelling media with periodic structure. The contribution deals with the classical definition, its problems, the “dual” definition based on the so-called periodic unfolding. Since in the case of domains with boundary the unfolding operator introduced by D.Cioranescu, A.Damlamian, G.Griso does not satisfy the crucial integral preserving prop- erty, the contribution proposes a modified unfolding operator which satisfies the property and thus simplifies the theory. The properties of two-scale convergence are surveyed.