Calculus of Variations and Geometric Measure Theory

S. Don - D. Vittone

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

created by vittone on 31 Aug 2018
modified on 17 Nov 2020


Published Paper

Inserted: 31 aug 2018
Last Updated: 17 nov 2020

Journal: J. Math. Anal. Appl.
Volume: 479
Pages: 482–530
Year: 2019

ArXiv: 1808.09711 PDF


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.