On formulae decoupling the total variation of BV functions
  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 $Du$. 
Augusto C. Ponce, Daniel Spector
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