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On formulae decoupling the total variation of bv functions

Daniel Spector National Chiao Tung University Augusto Ponce Catholique University of Louvain

Functional Analysis mathscidoc:1703.12005

Nonlinear Anal. , 154, 241–257., 2017
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 $Du$.
Bounded variation, Fractional Laplacian, Non-local energies
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@inproceedings{daniel2017on,
  title={ON FORMULAE DECOUPLING THE TOTAL VARIATION OF BV FUNCTIONS},
  author={Daniel Spector, and Augusto Ponce},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170309065850004019631},
  booktitle={Nonlinear Anal. },
  volume={154},
  pages={241–257.},
  year={2017},
}
Daniel Spector, and Augusto Ponce. ON FORMULAE DECOUPLING THE TOTAL VARIATION OF BV FUNCTIONS. 2017. Vol. 154. In Nonlinear Anal. . pp.241–257.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170309065850004019631.
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