Homogenization on perforated domains in SBV: an alternative approach

I will show a compactness result for sequence in SBV (the space of special functions of bounded variation). The main application is the homogenization of non-coercive functionals consisting of a volume and a surface integral.
More precisely, I will focus on the study of the asymptotic behaviour of the Mumford-Shah functional on a periodically perforated domain, as the size of the holes and the periodicity parameter of the structure tend to zero.

This is a joint work with M. Focardi.