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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.
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.
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