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arXiv · 2607.13751

Regularity estimates in transport equations via heat flow and quantitative differentiation

Elia Brué·Maria Colombo·Guido De Philippis·Carl Johan Peter Johansson
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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.

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Elia Brué, Maria Colombo, Guido De Philippis, Carl Johan Peter Johansson. 2026-07-15. Regularity estimates in transport equations via heat flow and quantitative differentiation. https://arxiv.org/abs/2607.13751

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