Inserted: 14 nov 2001
Ph.D. Thesis, SISSA, 2001 - Supervisor: Gianni Dal Maso
The calibration method is a minimality criterion, which has been adapted to the case of functionals with free discontinuties by Alberti, Bouchitté, and Dal Maso. In this thesis we apply this criterion to identify a wide class of non trivial minimizers for the Mumford-Shah functional. In the last part we develop the theory of calibrations for more general functionals with free discontinuities on vector-valued maps and we describe several applications of this result.