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arXiv · 1603.08663

On formulae decoupling the total variation of BV functions

Augusto C. Ponce·Daniel Spector
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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 $u\in SBV$ converge strictly to the singular portion of $Du$.

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Augusto C. Ponce, Daniel Spector. 2016-03-29. On formulae decoupling the total variation of BV functions. https://doi.org/10.1016/j.na.2016.08.028

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