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 on 24 Oct 2022


Accepted Paper

Inserted: 8 dec 2021
Last Updated: 24 oct 2022

Journal: Indiana Univ. Math. J.
Year: 2021

ArXiv: 2112.03832 PDF


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.