no. 2
Γ-limits of convolution functionals
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 486-515

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.

DOI : 10.1051/cocv/2012018
Classification : 49Q20, 49J45, 49M30
Keywords: free discontinuities, Γ-convergence, anisotropy 
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     title = {$\Gamma $-limits of convolution functionals},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {486--515},
     year = {2013},
     publisher = {EDP Sciences},
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     doi = {10.1051/cocv/2012018},
     zbl = {1263.49010},
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Lussardi, Luca; Magni, Annibale. $\Gamma $-limits of convolution functionals. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 486-515. doi: 10.1051/cocv/2012018

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