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arXiv · 1407.2023

BMO-type norms related to the perimeter of sets

Luigi Ambrosio·Jean Bourgain·Haim Brezis·Alessio Figalli
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Abstract

In this paper we consider an isotropic variant of the $BMO$-type norm recently introduced by Bourgain, Brezis and Mironescu. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.

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Luigi Ambrosio, Jean Bourgain, Haim Brezis, Alessio Figalli. 2014-07-08. BMO-type norms related to the perimeter of sets. https://arxiv.org/abs/1407.2023

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