English

On formulae decoupling the total variation of BV functions

Functional Analysis 2017-03-28 v2 Classical Analysis and ODEs

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 uSBVu\in SBV converge strictly to the singular portion of DuDu.

Keywords

Cite

@article{arxiv.1603.08663,
  title  = {On formulae decoupling the total variation of BV functions},
  author = {Augusto C. Ponce and Daniel Spector},
  journal= {arXiv preprint arXiv:1603.08663},
  year   = {2017}
}

Comments

17 pages

R2 v1 2026-06-22T13:20:16.035Z