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

TitleStable regular critical points of the Mumford-Shah functional are local minimizers
Publication TypeJournal Article
Year of Publication2015
AuthorsBonacini, M, Morini, M
JournalAnnales de l'Institut Henri Poincare (C) Non Linear Analysis
Volume32
Issue3
Start Page533
Pagination533-570
KeywordsMumford-Shah functional
Abstract

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.

URLhttps://www.sciencedirect.com/science/article/pii/S0294144914000171
DOI10.1016/j.anihpc.2014.01.006

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