Calculus of Variations and Geometric Measure Theory

G. Alberti - G. Bouchitté - G. Dal Maso

The calibration method for the Mumford-Shah functional and free-discontinuity problems

created on 13 Jun 2001
modified by alberti on 06 Mar 2007


Published Paper

Inserted: 13 jun 2001
Last Updated: 6 mar 2007

Journal: Calc. Var. Partial Differential Equations
Volume: 16
Number: 3
Pages: 299-333
Year: 2003


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. The preprint version ( contains some examples and remarks which were not included in the published version (file

Keywords: free discontinuity problems, special functions of bounded variation, Gradient Flow, Mumford-Shah functional, calibrations, necessary condition for minimality, minimal partitions