# MathSciDoc: An Archive for Mathematician ∫

#### Functional Analysismathscidoc:1703.12005

Nonlinear Anal. , 154, 241–257., 2017
In this paper we prove several formulae that enable one to capture the singular portion of the measure derivative of a function of bounded variation as a limit of non-local functionals. One special case shows that rescalings of the fractional Laplacian of a function $u \in SBV$ converge strictly to the singular portion of $Du$.
Bounded variation, Fractional Laplacian, Non-local energies
@inproceedings{daniel2017on,
title={ON FORMULAE DECOUPLING THE TOTAL VARIATION OF BV FUNCTIONS},
author={Daniel Spector, and Augusto Ponce},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170309065850004019631},
booktitle={Nonlinear Anal. },
volume={154},
pages={241–257.},
year={2017},
}

Daniel Spector, and Augusto Ponce. ON FORMULAE DECOUPLING THE TOTAL VARIATION OF BV FUNCTIONS. 2017. Vol. 154. In Nonlinear Anal. . pp.241–257.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170309065850004019631.