On formulae decoupling the total variation of BV functions

Augusto C. Ponce, Daniel Spector*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)241-257
Number of pages17
JournalNonlinear Analysis, Theory, Methods and Applications
Volume154
DOIs
Publication statusPublished - 2017 May 1
Externally publishedYes

Keywords

  • Bounded variation
  • Fractional Laplacian
  • Non-local energies

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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