Higher order pointwise differential for distribution
Classical Analysis and ODEs
2025-03-06 v3
Abstract
The notion of pointwise differentials for distributions is a way to extract local information of distributions by rescaling the distribution at a point. In this paper, we study the pointwise differentials for distributions corresponding to a negative order Sobolev functions. Our main results prove Borel regularity, Lusin approximation, rectifiability, and a Rademacher theorem for these pointwise differentials.
Cite
@article{arxiv.2412.17691,
title = {Higher order pointwise differential for distribution},
author = {Yu-Tong Liu},
journal= {arXiv preprint arXiv:2412.17691},
year = {2025}
}
Comments
33 pages, content unchange, acknowledgement update