Fine properties of functions with bounded variation in Carnot-Carath\'eodory spaces
Functional Analysis
2018-09-24 v2 Metric Geometry
Abstract
We study properties of functions with bounded variation in Carnot-Ca\-ra\-th\'eo\-do\-ry 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 , 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
Cite
@article{arxiv.1808.09711,
title = {Fine properties of functions with bounded variation in Carnot-Carath\'eodory spaces},
author = {Sebastiano Don and Davide Vittone},
journal= {arXiv preprint arXiv:1808.09711},
year = {2018}
}