Anisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionals
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1107-1139.

We provide an approximation result for free-discontinuity functionals of the form ( u ) = Ω f ( x , u , u ) d x + s u Ω θ ( x , ν u ) d n - 1 , u S B V 2 ( Ω )

where f is quadratic in the gradient-variable and θ is an arbitrary smooth Finsler metric. The approximating functionals are of Ambrosio-Tortorelli type and depend on the Hessian of the edge variable through a suitable nonhomogeneous metric ϕ .

DOI : 10.1051/cocv/2017027
Classification : 49J45, 74G65, 68U10
Mots clés : Γ-convergence, Ambrosio-Tortorelli approximation, anisotropic free-discontinuity functionals, Finsler metrics
Bach, Annika 1

1
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     title = {Anisotropic free-discontinuity functionals as the {\ensuremath{\Gamma}-limit} of second-order elliptic functionals},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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     publisher = {EDP-Sciences},
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Bach, Annika. Anisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionals. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1107-1139. doi : 10.1051/cocv/2017027. http://www.numdam.org/articles/10.1051/cocv/2017027/

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