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arXiv · 2610.29359

Lipschitz numbers and fine differentiability on metric measure spaces

Panu Lahti·Yuxin Li
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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.

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Panu Lahti, Yuxin Li. 2026-10-21. Lipschitz numbers and fine differentiability on metric measure spaces. https://arxiv.org/abs/2610.29359

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