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We approximate, in the sense of -convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.
@article{COCV_2007__13_1_135_0,
author = {Lussardi, Luca and Vitali, Enrico},
title = {Non-local approximation of free-discontinuity problems with linear growth},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {135--162},
publisher = {EDP-Sciences},
volume = {13},
number = {1},
year = {2007},
doi = {10.1051/cocv:2007008},
mrnumber = {2282106},
zbl = {1136.49029},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007008/}
}
TY - JOUR AU - Lussardi, Luca AU - Vitali, Enrico TI - Non-local approximation of free-discontinuity problems with linear growth JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 135 EP - 162 VL - 13 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007008/ DO - 10.1051/cocv:2007008 LA - en ID - COCV_2007__13_1_135_0 ER -
%0 Journal Article %A Lussardi, Luca %A Vitali, Enrico %T Non-local approximation of free-discontinuity problems with linear growth %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 135-162 %V 13 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007008/ %R 10.1051/cocv:2007008 %G en %F COCV_2007__13_1_135_0
Lussardi, Luca; Vitali, Enrico. Non-local approximation of free-discontinuity problems with linear growth. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 1, pp. 135-162. doi: 10.1051/cocv:2007008
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