Calculus of Variations and Geometric Measure Theory

L. Lussardi - E. Vitali

Non-local approximation of free-discontinuity problems with linear growth

created by vitali on 05 Jan 2006
modified on 03 Aug 2017


Published Paper

Inserted: 5 jan 2006
Last Updated: 3 aug 2017

Journal: ESAIM Control Optim. Calc. Var.
Volume: 13
Number: 1
Pages: 135
Year: 2007



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.