Regularity estimates in transport equations via heat flow and quantitative differentiation
arXiv:2607.13751
summary
The paper establishes quantitative estimates for commutators in transport equations, showing how logarithmic Sobolev regularity propagates via heat flow and using quantitative differentiation for the DiPerna‑Lions commutator.
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.
17 pages
Topics & keywords
#transport equations#regularity estimates#commutator analysis#heat flow#quantitative differentiation#sobolev regularityAmbrosio‑Trevisan commutatorDiPerna‑Lions commutatorlogarithmic Sobolevquantitative differentiationheat flowtransport PDE