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

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

ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 576-598.

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.

Classification : 49Q20, 49J45, 35B38, 35J60
Mots clés : Mumford-Shah functional, Ambrosio-Tortorelli functional, gamma-convergence, critical points, brittle fracture

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