Augusto C. Ponce, Daniel Spector
Published 2016-03-29Version 1
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 $Du$.
New estimates for a class of non-local approximations of the total variation
On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation
An extension of the pairing theory between divergence-measure fields and BV functions
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