Geodesic
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

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We provide an approximation result for free-discontinuity functionals of the form ℱ ( u ) = ∫ Ω f ( x , u , ∇ u ) d x + ∫ s u ∩ Ω θ ( x , ν u ) d ℋ 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
Keywords: Γ-convergence, Ambrosio-Tortorelli approximation, anisotropic free-discontinuity functionals, Finsler metrics

Bach, Annika 1

1 
@article{COCV_2018__24_3_1107_0,
     author = {Bach, Annika},
     title = {Anisotropic free-discontinuity functionals as the {\ensuremath{\Gamma}-limit} of second-order elliptic functionals},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1107--1139},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {3},
     year = {2018},
     doi = {10.1051/cocv/2017027},
     zbl = {1412.49032},
     mrnumber = {3877195},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017027/}
}
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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

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