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

Article type: Research Article

Authors: Amar, M.

Affiliations: Dipartimento di Matematica, Università di Pavia, Via Abbiategrasso 209, 27100 Pavia, Italy Email: amar@dragon.ian.pv.cnr.it

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.

Keywords: 2‐scale convergence, measures, [TeX:] BV‐functions, homogenization

Journal: Asymptotic Analysis, vol. 16, no. 1, pp. 65-84, 1998