Stable regular critical points of the Mumford–Shah functional are local minimizers
Marco Bonacini, Massimiliano Morini · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2014
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. A global minimality result in small tubular neighborhoods of the discontinuity set is also established.