Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators

Journal de l’École polytechnique — Mathématiques 2026 Open access

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Authors: Francesca Anceschi, Helge Dietert, Jessica Guerand, Amélie Loher, Clément Mouhot, Annalaura Rebucci
DOI: 10.5802/jep.350
Cited by: 0

Abstract

We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörmander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak Harnack inequality and Hölder regularity along the line of the De Giorgi method.

Fields of Study & Subjects

Spectral Theory in Mathematical Physics advanced mathematical theories Differential Equations and Boundary Problems

Publication details

Journal / source
Journal de l’École polytechnique — Mathématiques
Volume
13
Pages
1393–1417
Publication date
31 August 2026
Language
EN