CRITICAL POINTS OF AMBROSIO-TORTORELLI CONVERGE TO CRITICAL POINTS OF MUMFORD-SHAH IN THE ONE-DIMENSIONAL DIRICHLET CASE

被引：15

作者：

Francfort, Gilles A. ^{[1
]}

Le, Nam Q. ^{[2
]}

Serfaty, Sylvia ^{[2
]}

机构：

[1] Univ Paris 13, LPMTM, F-93430 Villetaneuse, France

[2] Courant Inst Math Sci, New York, NY 10012 USA

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2009年 / 15卷 / 03期

关键词：

Mumford-Shah functional; Ambrosio-Tortorelli functional; Gamma-convergence; critical points; brittle fracture; VARIATIONAL-PROBLEMS; BRITTLE-FRACTURE; APPROXIMATION;

D O I：

10.1051/cocv:2008041

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.

引用

页码：576 / 598

页数：23

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