Calculus of Variations and Geometric Measure Theory

G. E. Comi

$BMO$-type norms and anisotropic surface measures

created by comi on 17 May 2018
modified on 29 May 2020

[BibTeX]

Published Paper

Inserted: 17 may 2018
Last Updated: 29 may 2020

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 J. Bourgain, H. Brezis, P. Mironescu: A new function space and applications. Journal of the EMS, 17 (2015), 2083-2101, 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 L. Ambrosio, H. Brezis, J. Bourgain, A. Figalli: BMO-type norms related to the perimeter of sets, Comm. Pure Appl. Math., 69 (2016), 1062-1086.

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


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