cvgmt: Representation of the total variation as a $Γ$-limit of $BMO$-type seminorms

Calculus of Variations and Geometric Measure Theory

A. Arroyo-Rabasa - P. Bonicatto - G. Del Nin

Representation of the total variation as a $Γ$-limit of $BMO$-type seminorms

created by delnin on 08 Dec 2021
modified by bonicatto on 23 Dec 2025

[BibTeX]

Published Paper

Inserted: 8 dec 2021
Last Updated: 23 dec 2025

Journal: Indiana Univ. Math. J.
Volume: 73
Pages: 341–365
Year: 2024

Abstract:

We address a question raised by Ambrosio, Bourgain, Brezis, and Figalli, proving that the $\Gamma$-limit, with respect to the $L^1_{\rm loc}$ topology, of a family of $BMO$-type seminorms is given by $\tfrac14$ times the total variation seminorm.