In this paper we consider an isotropic variant of the BMO-type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). 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.
BMO-Type Norms Related to the Perimeter of Sets
AMBROSIO, Luigi;FIGALLI, ALESSIO
2016
Abstract
In this paper we consider an isotropic variant of the BMO-type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). 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.File in questo prodotto:
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