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ambrosio-tortorelli functional

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Critical points of Ambrosio-Tortorelli convergeto critical points of Mumford-Shahin the one-dimensional Dirichlet case
Gilles A. Francfort, Nam Q. Le, Sylvia Serfaty
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 15 / Issue 3 / July 2009

Published online by Cambridge University Press:

24 June 2008, pp. 576-598

Print publication:

July 2009
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Critical points of a variant of the Ambrosio-Tortorelli functional,for which non-zero Dirichlet boundary conditions replace thefidelity term, are investigated. They are shown to converge toparticular critical points of the corresponding variant of theMumford-Shah functional; those exhibit many symmetries. ThatDirichlet variant is the natural functional when addressing aproblem of brittle fracture in an elastic material.