We approximate, in the sense of $\Gamma $-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.

Keywords: variational approximation, free discontinuities

@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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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, Volume 13 (2007) no. 1, pp. 135-162. doi : 10.1051/cocv:2007008. http://archive.numdam.org/articles/10.1051/cocv:2007008/

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