Inserted: 25 jul 2013
Last Updated: 22 feb 2014
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
In this paper it is shown that any regular critical point of the Mumford-Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$-topology.
Keywords: Free-discontinuity problems, Mumford-Shah functional, second variation, local minimality conditions