Calculus of Variations and Geometric Measure Theory

F. Nobili - E. Pasqualetto - T. Schultz

On master test plans for the space of BV functions

created by pasqualetto on 13 Sep 2021
modified by nobili on 31 May 2022


Published Paper

Inserted: 13 sep 2021
Last Updated: 31 may 2022

Journal: Adv. Calc. Var.
Year: 2022
Doi: 10.1515/acv-2021-0078

ArXiv: 2109.04980 PDF


We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all $\rm BV$ functions and their total variation measures. In the setting of non-branching ${\sf CD}(K,N)$ spaces (with finite reference measure), we can additionally require these test plans to be concentrated on geodesics.