Volume 15, Number 3, July-September 2009
|Page(s)||576 - 598|
|Published online||24 June 2008|
Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
LPMTM, Université Paris 13,
Av. J.B. Clément, 93430 Villetaneuse, France. firstname.lastname@example.org
2 Courant Institute of Mathematical Sciences, 251 Mercer St, New York, NY 10012, USA. email@example.com
3 Courant Institute of Mathematical Sciences, 251 Mercer St, New York, NY 10012, USA. firstname.lastname@example.org
Revised: 29 February 2008
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.
Mathematics Subject Classification: 49Q20 / 49J45 / 35B38 / 35J60
Key words: Mumford-Shah functional / Ambrosio-Tortorelli functional / Gamma-convergence / critical points / brittle fracture
© EDP Sciences, SMAI, 2008
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