# $BMO$-type norms and anisotropic surface measures

created by comi on 17 May 2018

[BibTeX]

Accepted Paper

Inserted: 17 may 2018
Last Updated: 17 may 2018

Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Volume: 29
Number: 3
Pages: 431-437
Year: 2018
Doi: 10.4171/RLM/815

Abstract:

The purpose of this note is to present an anisotropic variant of the $BMO$-type norm introduced by Bourgain, Brezis and Mironescu, and to show its relation with a surface measure, which is indeed a multiple of the perimeter in the isotropic case. This is done in the spirit of the new characterization of the perimeter of a measurable set in $\mathbb{R}^{n}$ recently studied by Ambrosio, Bourgain, Brezis and Figalli.