Multiple-scale homogenization problems are treated in the space $BV$ of functions of bounded variation, using the notion of multiple-scale convergence developed in [R. Ferreira and I. Fonseca, J. Convex Anal., to appear]. In the case of one microscale, Amar’s result [Asymptot. Anal., 16 (1998), pp. 65–84] is recovered under more general conditions; for two or more microscales, new results are obtained.
