On formulae decoupling the total variation of BV functions

Augusto C. Ponce; Daniel Spector

doi:10.1016/j.na.2016.08.028

On formulae decoupling the total variation of BV functions

Augusto C. Ponce
, Daniel Spector^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 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 language	English
Pages (from-to)	241-257
Number of pages	17
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	154
DOIs	https://doi.org/10.1016/j.na.2016.08.028
Publication status	Published - 2017 May 1
Externally published	Yes

Keywords

Bounded variation
Fractional Laplacian
Non-local energies

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2016.08.028

Cite this

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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 = "Publisher Copyright: {\textcopyright} 2016 Elsevier Ltd",

year = "2017",

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day = "1",

doi = "10.1016/j.na.2016.08.028",

language = "English",

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T1 - On formulae decoupling the total variation of BV functions

AU - Ponce, Augusto C.

AU - Spector, Daniel

PY - 2017/5/1

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N2 - 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.

AB - 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.

KW - Bounded variation

KW - Fractional Laplacian

KW - Non-local energies

UR - https://www.scopus.com/pages/publications/84995693918

UR - https://www.scopus.com/pages/publications/84995693918#tab=citedBy

U2 - 10.1016/j.na.2016.08.028

DO - 10.1016/j.na.2016.08.028

M3 - Article

AN - SCOPUS:84995693918

SN - 0362-546X

VL - 154

SP - 241

EP - 257

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

On formulae decoupling the total variation of BV functions

Abstract

Keywords

ASJC Scopus subject areas

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