L On formulae decoupling the total variation of BV functions

Abstract

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 is an element of SBV converge strictly to the singular portion of D-u. (C) 2016 Elsevier Ltd. All rights reserved.