We consider the family of non-local and non-convex functionals introduced by H. Brézis 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.
Antonucci, C., Gobbino, M., Migliorini, M., Picenni, N. (2018). On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation. COMPTES RENDUS MATHÉMATIQUE, 356(8), 859-864 [10.1016/j.crma.2018.05.014].
On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation
Picenni, Nicola
2018-01-01
Abstract
We consider the family of non-local and non-convex functionals introduced by H. Brézis 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.| File | Dimensione | Formato | |
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