02147nas a2200157 4500008004100000245008700041210006900128260001000197300001200207490000700219520161800226653002801844100002001872700002501892856007201917 2015 en d00aStable regular critical points of the Mumford-Shah functional are local minimizers0 aStable regular critical points of the MumfordShah functional are bSISSA a533-5700 v323 a

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.

10aMumford-Shah functional1 aBonacini, Marco1 aMorini, Massimiliano uhttps://www.sciencedirect.com/science/article/pii/S0294144914000171