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<p>We study a class of non-local functionals that was introduced by Brezis et al. (Atti Accad Naz Lincei Rend Lincei Mat Appl 33(2):413–437, 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月5日

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  • Panu Lahti

摘要

We study a class of non-local functionals that was introduced by Brezis et al. (Atti Accad Naz Lincei Rend Lincei Mat Appl 33(2):413–437, 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.