@article{9df9f2ccceba47b2866348995a73d57d,
title = "On formulae decoupling the total variation of BV functions",
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.",
keywords = "Bounded variation, Fractional Laplacian, Non-local energies",
author = "Ponce, {Augusto C.} and Daniel Spector",
note = "Funding Information: The authors would like to thank the referee for his or her detailed reading and comments that have improved the quality of the presentation of the paper. This work was initiated while the first author (ACP) was visiting the Department of Applied Mathematics of the National Chiao Tung University (Research Grant 104W986 ). He warmly thanks the Department for the invitation and hospitality; he has also been supported by the Fonds de la Recherche scientifique–FNRS under research grant J.0026.15 . The second author (DS) is supported by the Taiwan Ministry of Science and Technology under research grants 103-2115-M-009-016-MY2 and 105-2115-M-009-004-MY2 . Publisher Copyright: {\textcopyright} 2016 Elsevier Ltd",
year = "2017",
month = may,
day = "1",
doi = "10.1016/j.na.2016.08.028",
language = "English",
volume = "154",
pages = "241--257",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
}