Calculus of Variations and Geometric Measure Theory

D. Spector - A. Ponce

On formulae decoupling the total variation of BV functions

created by spector on 29 Mar 2016
modified on 31 Aug 2016



Inserted: 29 mar 2016
Last Updated: 31 aug 2016

Year: 2016


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 $Du$.