Regularity estimates in transport equations via heat flow and quantitative differentiation
Analysis of PDEs
2026-07-15 v1
Abstract
The purpose of this note is twofold. First, we prove quantitative estimates for the Ambrosio-Trevisan commutator which implies propagation of logarithmic Sobolev regularity. Second, we prove a similar estimate for the DiPerna-Lions commutator by relying on quantitative differentiation.
Cite
@article{arxiv.2607.13751,
title = {Regularity estimates in transport equations via heat flow and quantitative differentiation},
author = {Elia Brué and Maria Colombo and Guido De Philippis and Carl Johan Peter Johansson},
journal= {arXiv preprint arXiv:2607.13751},
year = {2026}
}
Comments
17 pages