# Fine properties of functions with bounded variation in Carnot-Carathéodory spaces

created by vittone on 31 Aug 2018
modified on 21 Sep 2018

[BibTeX]

preprint

Inserted: 31 aug 2018
Last Updated: 21 sep 2018

Year: 2018

ArXiv: 1808.09711 PDF

Abstract:

We study properties of functions with bounded variation in Carnot-Carath\'eodory 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 $\mathcal R$, we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.