English

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 R\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.

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}
}