Non-local approximation of free-discontinuity problems with linear growth
Dipartimento di Matematica “F. Casorati”
Via Ferrata 1, 27100, Pavia, Italy;
Revised: 22 November 2005
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.
Mathematics Subject Classification: 49Q20 / 49J45 / 49M30
Key words: Variational approximation / free discontinuities.
© EDP Sciences, SMAI, 2007