Calculus of Variations and Geometric Measure Theory

M. Di Marco

Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces

created by dimarco on 23 Oct 2025

[BibTeX]

preprint

Inserted: 23 oct 2025

Year: 2025

ArXiv: 2510.19380 PDF

Abstract:

By introducing an intrinsic perimeter measure for intrinsic countably rectifiable sets, we prove a compactness result and a Poincar\'e inequality for special functions with bounded variation in equiregular Carnot-Carath\'eodory spaces which satisfy an additional natural assumption, called property $\mathcal R$.