Two-scale convergence and homogenization on BV(Omega)

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