a1 LPMTM, Université Paris 13, Av. J.B. Clément, 93430 Villetaneuse, France. firstname.lastname@example.org
a2 Courant Institute of Mathematical Sciences, 251 Mercer St, New York, NY 10012, USA. email@example.com
a3 Courant Institute of Mathematical Sciences, 251 Mercer St, New York, NY 10012, USA. firstname.lastname@example.org
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.
(Received September 19 2007)
(Revised February 29 2008)
(Online publication June 24 2008)
Mathematics Subject Classification: