A formula for the anisotropic total variation of SBV functions

The purpose of this paper is to present the relation between certain BMO–type seminorms and the total variation of SBV functions. Following some ideas of [2], we give a representation formula of the total variation of SBV functions which does not make use of the distributional derivatives. We consid...

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Bibliographic Details
Published in:Journal of functional analysis 2020-05, Vol.278 (9), p.108451, Article 108451
Main Authors: Farroni, Fernando, Fusco, Nicola, Guarino Lo Bianco, Serena, Schiattarella, Roberta
Format: Article
Language:English
Subjects:
BMO-type seminorms
Special functions of bounded variations
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Summary:The purpose of this paper is to present the relation between certain BMO–type seminorms and the total variation of SBV functions. Following some ideas of [2], we give a representation formula of the total variation of SBV functions which does not make use of the distributional derivatives. We consider an anisotropic variant of the BMO–type seminorm introduced in [4], by using, instead of cubes, covering families made by translations of a given open bounded set with Lipschitz boundary.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2019.108451