On formulae decoupling the total variation of BV functions. (May 2017) - Ponce, Augusto C.; Spector, Daniel
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 ∈ S B V converge strictly to the singular portion of D u .