Fine properties of functions with bounded variation in Carnot-Carathéodory spaces
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.
Main Authors
Format
Articles
Research article
Published
2019
Series
Subjects
Publication in research information system
Publisher
Academic Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201909023999Use this for linking
Review status
Peer reviewed
ISSN
0022-247X
DOI
https://doi.org/10.1016/j.jmaa.2019.06.035
Language
English
Published in
Journal of Mathematical Analysis and Applications
Citation
- 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
License
Funder(s)
Academy of Finland
European Commission
Funding program(s)
Akatemiatutkija, SA
ERC Starting Grant
Academy Research Fellow, AoF
ERC Starting Grant
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
The authors are supported by the University of Padova Project Networking and STARS Project “Sub-Riemannian Geometry and Geometric Measure Theory Issues: Old and New” (SUGGESTION), and by GNAMPA of INdAM (Italy) project “Campi vettoriali, superfici e perimetri in geometrie singolari”. The second named author wishes to acknowledge the support and hospitality of FBK-CIRM (Trento), where part of this paper was written. The first named author has been partially supported by the Academy of Finland (grant 288501 “Geometry of subRiemannian groups”) and by the European Research Council (ERC Starting Grant 713998 GeoMeG “Geometry of Metric Groups”).
Copyright© 2019 Elsevier Inc.