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arXiv · 1801.04591

On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation

Clara Antonucci·Massimo Gobbino·Matteo Migliorini·Nicola Picenni
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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.

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Clara Antonucci, Massimo Gobbino, Matteo Migliorini, Nicola Picenni. 2018-01-14. On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation. https://arxiv.org/abs/1801.04591

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