A1 Journal article (refereed)
Fine properties of functions with bounded variation in Carnot-Carathéodory spaces (2019)
Don, S., & Vittone, D. (2019). Fine properties of functions with bounded variation in Carnot-Carathéodory spaces. Journal of Mathematical Analysis and Applications, 479 (1), 482-530. doi:10.1016/j.jmaa.2019.06.035
JYU authors or editors
Publication details
All authors or editors: Don, Sebastiano; Vittone, Davide
Journal or series: Journal of Mathematical Analysis and Applications
ISSN: 0022-247X
eISSN: 1096-0813
Publication year: 2019
Volume: 479
Issue number: 1
Pages range: 482-530
Publisher: Academic Press
Publication country: United States
Publication language: English
DOI: https://doi.org/10.1016/j.jmaa.2019.06.035
Open Access: Publication channel is not openly available
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/65426
Publication is parallel published: https://arxiv.org/abs/1808.09711
Abstract
We study properties of functions with bounded variation in Carnot-Carathéodory spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R, we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.
Keywords: functions (mathematical methods); differential geometry; calculus of variations; measure theory
Free keywords: functions with bounded variation; Carnot-Carathéodory spaces
Contributing organizations
Related projects
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- European Commission
Ministry reporting: Yes
Reporting Year: 2019
JUFO rating: 1