A sharp lower bound for a class of non-local approximations of the total variation

2023/10/05 by Panu Lahti, Lahti, Panu
Mathematics · #26A46 #26B30 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2310.03550

openalex publication_date 2023/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a class of non-local functionals that was introduced by Brezis-Seeger-Van Schaftingen-Yung (2022), and can be used to characterize functions of bounded variation. We give a new lower bound for the liminf of these functionals, involving the three different parts of the total variation, with sharp coefficients.

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