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

被引：9

作者：

Bonacini, M. ^{[1
]}

Morini, M. ^{[2
]}

机构：

[1] SISSA, I-34136 Trieste, Italy

[2] Univ Parma, Dipartimento Matemat, I-43100 Parma, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2015年 / 32卷 / 03期

关键词：

Mumford-Shah functional; Free discontinuity problems; Second variation; EXISTENCE THEOREM; CALIBRATIONS; MINIMALITY;

D O I：

10.1016/j.anihpc.2014.01.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2014 Elsevier Masson SAS. All rights reserved.

引用

页码：533 / 570

页数：38

共 25 条

[1] Minimality via Second Variation for a Nonlocal Isoperimetric Problem [J].