English

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}
}

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17 pages