C. Antonucci - M. Gobbino - M. Migliorini - N. Picenni
On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation
Published Paper
Inserted: 24 aug 2023
Last Updated: 30 oct 2023
Journal: C. R. Math. Acad. Sci. Paris
Year: 2018
Doi: https://doi.org/10.1016/j.crma.2018.05.014
Abstract:
We consider the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sobolev norm or the total variation, depending on a summability exponent, but the exact values of the constants are unknown in many cases. We describe a new approach to the Gamma-convergence result that leads in some special cases to the exact value of the constants, and to the existence of smooth recovery families.