Filippo Cagnetti, SISSA, Visiting Scholar
An Extension Theorem in SBV
We show the existence of an extension operator for special functions with bounded variation with a careful energy estimate. The main application is a compactness result for non-coercive functionals consisting of a volume and a surface integral. More precisely, we 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.
TUESDAY, February 12, 2008