We provide an approximation result for free-discontinuity functionals of the form
where is quadratic in the gradient-variable and 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 .
Keywords: Γ-convergence, Ambrosio-Tortorelli approximation, anisotropic free-discontinuity functionals, Finsler metrics
Bach, Annika 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},
year = {2018},
publisher = {EDP Sciences},
volume = {24},
number = {3},
doi = {10.1051/cocv/2017027},
zbl = {1412.49032},
mrnumber = {3877195},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2017027/}
}
TY - JOUR AU - Bach, Annika TI - Anisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionals JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1107 EP - 1139 VL - 24 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2017027/ DO - 10.1051/cocv/2017027 LA - en ID - COCV_2018__24_3_1107_0 ER -
%0 Journal Article %A Bach, Annika %T Anisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionals %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1107-1139 %V 24 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2017027/ %R 10.1051/cocv/2017027 %G en %F COCV_2018__24_3_1107_0
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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