Poincar\'e inequality and quantitative De Giorgi method for hypoelliptic operators
Analysis of PDEs
2025-08-07 v3
Abstract
We propose a systematic approach based on trajectories to prove a Poincar\'e inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of H\"ormander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak Harnack inequality and H\"older regularity along the line of the De Giorgi method.
Cite
@article{arxiv.2401.12194,
title = {Poincar\'e inequality and quantitative De Giorgi method for hypoelliptic operators},
author = {Francesca Anceschi and Helge Dietert and Jessica Guerand and Amélie Loher and Clément Mouhot and Annalaura Rebucci},
journal= {arXiv preprint arXiv:2401.12194},
year = {2025}
}
Comments
23 pages, 4 figures. Rewrote the introduction and clarified the ellipticity assumption