@article {2003, title = {The calibration method for the Mumford-Shah functional and free-discontinuity problems}, journal = {Calc. Var. Partial Differential Equations 16 (2003) 299-333}, number = {SISSA;35/2001/M}, year = {2003}, publisher = {Springer}, abstract = {We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.}, doi = {10.1007/s005260100152}, url = {http://hdl.handle.net/1963/3051}, author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso} } @article {1999, title = {The calibration method for the Mumford-Shah functional}, journal = {C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254}, number = {SISSA;21/99/M}, year = {1999}, publisher = {Elsevier}, abstract = {In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3).}, doi = {10.1016/S0764-4442(00)88602-4}, url = {http://hdl.handle.net/1963/1235}, author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso} }