Calculus of Variations and Geometric Measure Theory
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G. E. Comi

$BMO$-type norms and anisotropic surface measures

created by comi on 17 May 2018


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


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.

Keywords: sets of finite perimeter, anisotropic perimeter, sphere packing problem


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