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. https://doi.org/10.1016/j.jmaa.2019.06.035

JYU authors or editors

Don, Sebastiano

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

Publication open access: Not open

Publication channel open access:

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

Fields of science: