On formulae decoupling the total variation of BV functions

Ponce, Augusto;Spector, Daniel
(2017) Nonlinear Analysis: Theory, Methods & Applications — Vol. 154, p. 241-257 (2017)

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  • Ponce, Augustoorcid-logoUCLouvain
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  • Spector, DanielNational Chiao Tung University, Department of Applied Mathematics, Hsinchu, Taiwan
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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∈SBV converge strictly to the singular portion of Du.
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Ponce, A., & Spector, D. (2017). On formulae decoupling the total variation of BV functions. Nonlinear Analysis: Theory, Methods & Applications, 154, 241-257. https://doi.org/10.1016/j.na.2016.08.028 (Original work published 2017)