TY - JOUR T1 - The calibration method for the Mumford-Shah functional and free-discontinuity problems JF - Calc. Var. Partial Differential Equations 16 (2003) 299-333 Y1 - 2003 A1 - Giovanni Alberti A1 - Guy Bouchitte A1 - Gianni Dal Maso AB - 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. PB - Springer UR - http://hdl.handle.net/1963/3051 U1 - 1282 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The calibration method for the Mumford-Shah functional JF - C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 Y1 - 1999 A1 - Giovanni Alberti A1 - Guy Bouchitte A1 - Gianni Dal Maso AB - 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). PB - Elsevier UR - http://hdl.handle.net/1963/1235 U1 - 2708 U2 - Mathematics U3 - Functional Analysis and Applications ER -