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/S029414491400017100979nas a2200157 4500008004100000022004000041245009000081210006900171260001900240300001200259490000600271520039700277653003900674100002000713856008800733 2014 en d aOnline: 1864-8266; Print: 1864-825800aStability of equilibrium configurations for elastic films in two and three dimensions0 aStability of equilibrium configurations for elastic films in two bSISSAc01/2014 a117-1530 v83 a

We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

10aEpitaxially strained elastic films1 aBonacini, Marco uhttps://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml