Calculus of Variations and Geometric Measure Theory

M. Bonacini - M. Morini

Stable regular critical points of the Mumford-Shah functional are local minimizers

created by bonacini on 25 Jul 2013
modified on 22 Feb 2014


Accepted Paper

Inserted: 25 jul 2013
Last Updated: 22 feb 2014

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2014
Doi: 10.1016/j.anihpc.2014.01.006


In this paper it is shown that any regular critical point of the Mumford-Shah functional, with positive de finite 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