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 a recent paper by L. Ambrosio and G.E. Comi, 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 2015 in a paper by J. Bourgain, H. Brezis and P. Mironescu, by using, instead of cubes, covering families made by translations of a given open bounded set with Lipschitz boundary.
A formula for the anisotropic total variation of SBV functions / Farroni, Fernando; Fusco, Nicola; GUARINO LO BIANCO, Serena; Schiattarella, Roberta. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 278:9(2020), pp. 1-32. [10.1016/j.jfa.2019.108451]
A formula for the anisotropic total variation of SBV functions
Fernando Farroni;Nicola Fusco
;Serena Guarino Lo Bianco;Roberta Schiattarella
2020
Abstract
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 a recent paper by L. Ambrosio and G.E. Comi, 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 2015 in a paper by J. Bourgain, H. Brezis and P. Mironescu, by using, instead of cubes, covering families made by translations of a given open bounded set with Lipschitz boundary.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
