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arXiv · 2401.12194

Poincar\'e inequality and quantitative De Giorgi method for hypoelliptic operators

Francesca Anceschi·Helge Dietert·Jessica Guerand·Amélie Loher·Clément Mouhot·Annalaura Rebucci
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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.

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Francesca Anceschi, Helge Dietert, Jessica Guerand, Amélie Loher, Clément Mouhot, Annalaura Rebucci. 2024-01-22. Poincar\'e inequality and quantitative De Giorgi method for hypoelliptic operators. https://arxiv.org/abs/2401.12194

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