Non-local approximation of free-discontinuity problems with linear growth
Luca Lussardi, Enrico Vitali · ESAIM Control Optimisation and Calculus of Variations · 2007
We approximate, in the sense of Γ-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.