Two‐scale convergence and homogenization on $BV(\varOmega)$

Abstract

We extend the notion of two‐scale convergence introduced by G. Nguetseng and G. Allaire to the case of sequences of bounded Radon measures. We prove a compactness result for two‐scale convergence. We then apply it to the study of the asymptotic behaviour of sequences of positively 1‐homogeneus and periodically oscillating functionals with linear growth, defined on the space $BV$ of the functions with bounded total variation.