We compute the Γ-limit of a sequence of non-local integral functionals depending on a regularization of the gradient term by means of a convolution kernel. In particular, as Γ-limit, we obtain free discontinuity functionals with linear growth and with anisotropic surface energy density.
Keywords: free discontinuities, Γ-convergence, anisotropy
@article{COCV_2013__19_2_486_0, author = {Lussardi, Luca and Magni, Annibale}, title = {$\Gamma $-limits of convolution functionals}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {486--515}, publisher = {EDP-Sciences}, volume = {19}, number = {2}, year = {2013}, doi = {10.1051/cocv/2012018}, zbl = {1263.49010}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2012018/} }
TY - JOUR AU - Lussardi, Luca AU - Magni, Annibale TI - $\Gamma $-limits of convolution functionals JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 486 EP - 515 VL - 19 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012018/ DO - 10.1051/cocv/2012018 LA - en ID - COCV_2013__19_2_486_0 ER -
%0 Journal Article %A Lussardi, Luca %A Magni, Annibale %T $\Gamma $-limits of convolution functionals %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 486-515 %V 19 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012018/ %R 10.1051/cocv/2012018 %G en %F COCV_2013__19_2_486_0
Lussardi, Luca; Magni, Annibale. $\Gamma $-limits of convolution functionals. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 2, pp. 486-515. doi : 10.1051/cocv/2012018. http://www.numdam.org/articles/10.1051/cocv/2012018/
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