# Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case

Gilles A. Francfort; Nam Q. Le; Sylvia Serfaty

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- Volume: 15, Issue: 3, page 576-598
- ISSN: 1292-8119

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topFrancfort, Gilles A., Le, Nam Q., and Serfaty, Sylvia. "Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case." ESAIM: Control, Optimisation and Calculus of Variations 15.3 (2009): 576-598. <http://eudml.org/doc/245594>.

@article{Francfort2009,

abstract = {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.},

author = {Francfort, Gilles A., Le, Nam Q., Serfaty, Sylvia},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Mumford-Shah functional; Ambrosio-Tortorelli functional; gamma-convergence; critical points; brittle fracture; -convergence},

language = {eng},

number = {3},

pages = {576-598},

publisher = {EDP-Sciences},

title = {Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case},

url = {http://eudml.org/doc/245594},

volume = {15},

year = {2009},

}

TY - JOUR

AU - Francfort, Gilles A.

AU - Le, Nam Q.

AU - Serfaty, Sylvia

TI - Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2009

PB - EDP-Sciences

VL - 15

IS - 3

SP - 576

EP - 598

AB - 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.

LA - eng

KW - Mumford-Shah functional; Ambrosio-Tortorelli functional; gamma-convergence; critical points; brittle fracture; -convergence

UR - http://eudml.org/doc/245594

ER -

## References

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