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.
Lussardi, L., Vitali, E., NON LOCAL APPROXIMATION OF FREE DISCONTINUITY PROBLEMS WITH LINEAR GROWTH, <<ESAIM. COCV>>, 2007; 13 (1): 135-162. [doi:10.1051/cocv:2007008] [http://hdl.handle.net/10807/1973]
NON LOCAL APPROXIMATION OF FREE DISCONTINUITY PROBLEMS WITH LINEAR GROWTH
Lussardi, Luca;
2007
Abstract
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.
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