Year: 2026
Type: preprint
Abstract: On a metric space equipped with a doubling measure supporting a Poincaré inequality, we introduce capacity-relaxed infinitesimal Lipschitz numbers and characterize Newtonian functions in $N^{1,p}$, $1\le p\le\infty$, and functions of bounded variation. If $X$ is additionally $Q$-regular, then every BV function is $1$-finely differentiable at $μ$-almost every point, and its fine differential agrees with its approximate Cheeger differential. We also extend a Sobolev regularity criterion from continuous to $p$-quasicontinuous functions.
Source: arXiv (Cornell University)
Authors: Lahti, Panu, Li, Yuxin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223226022