| Issue |
ESAIM: COCV
Volume 24, Number 3, July–September 2018
|
|
|---|---|---|
| Page(s) | 1107 - 1139 | |
| DOI | https://doi.org/10.1051/cocv/2017027 | |
| Published online | 15 June 2018 | |
Anisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionals
Angewandte Mathematik, Westfälische Wilhelms-Universität Münster,
Einsteinstr. 62,
48149
Münster, Germany
a Corresponding author: a_bach10@uni-muenster.de
Received:
10
October
2016
Accepted:
17
March
2017
We provide an approximation result for free-discontinuity functionals of the form
𝓕(u) = ∫Ωf(x, u, ∇u)dx + ∫Su∩Ωθ(x, νu)d𝓗n−1, u ∈ SBV2(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.
Mathematics Subject Classification: 49J45 / 74G65 / 68U10
Key words: Γ-convergence / Ambrosio-Tortorelli approximation / anisotropic free-discontinuity functionals / Finsler metrics
© EDP Sciences, SMAI 2018
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