commutator analysis 1heat flow 1quantitative differentiation 1regularity estimates 1sobolev regularity 1transport equations 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.AP2026
Regularity estimates in transport equations via heat flow and quantitative differentiation
Elia Brué, Maria Colombo, Guido De Philippis +1
The paper establishes quantitative estimates for commutators in transport equations, showing how logarithmic Sobolev regularity propagates via heat flow and using quantitative diff…
math.DG2026
Topology of two-dimensional collapsed spaces with lower Ricci bounds
Elia Bruè, Qin Deng
We prove that collapsed metric measure spaces with Ricci curvature bounded below and essential dimension two are topological surfaces, possibly with boundary.
math.AP2025
Lyapunov exponents, entropy and mixing for DiPerna-Lions flows
Elia Brué, Maria Colombo, Carl Johan Peter Johansson
The main goal of this work is to establish an asymptotic form of Bressan's mixing conjecture. To this end, we develop an ergodic-theoretic framework for incompressible DiPerna-Lion…