Calculus of Variations and Geometric Measure Theory

L. Ambrosio - H. Brezis - J. Bourgain - A. Figalli

$BMO$-type norms related to the perimeter of sets

created by ambrosio on 08 Jul 2014
modified by figalli on 04 Mar 2015


Accepted Paper

Inserted: 8 jul 2014
Last Updated: 4 mar 2015

Journal: Comm. Pure Appl. Math.
Year: 2015


In this paper we consider an isotropic variant of the $BMO$-type norm recently introduced in a recent work 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.

Tags: GeMeThNES