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

2018/01/14 by Clara Antonucci, Massimo Gobbino, Antonucci, Clara +5
Mathematics · #26B30 #46E35 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1801.04591

openalex publication_date 2018/01/14 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider the family of non-local and non-convex functionals introduced by\nH. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge\nto a multiple of the Sobolev norm or the total variation, depending on a\nsummability exponent, but the exact values of the constants are unknown in many\ncases.\n We describe a new approach to the Gamma-convergence result that leads in some\nspecial cases to the exact value of the constants, and to the existence of\nsmooth recovery families.\n

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