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.

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.

DOI : https://doi.org/10.1051/cocv:2007008
Classification : 49Q20,  49J45,  49M30
Mots clés : variational approximation, free discontinuities
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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. http://www.numdam.org/articles/10.1051/cocv:2007008/

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