Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Anceschi, Francesca, Dietert, Helge, Guerand, Jessica, Loher, Amélie, Mouhot, Clément, Rebucci, Annalaura
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916883506135040
author Anceschi, Francesca
Dietert, Helge
Guerand, Jessica
Loher, Amélie
Mouhot, Clément
Rebucci, Annalaura
author_facet Anceschi, Francesca
Dietert, Helge
Guerand, Jessica
Loher, Amélie
Mouhot, Clément
Rebucci, Annalaura
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_12194
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
Anceschi, Francesca
Dietert, Helge
Guerand, Jessica
Loher, Amélie
Mouhot, Clément
Rebucci, Annalaura
Analysis of PDEs
35K70, 35H10, 35B65, 35B45, 35A23
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.
title Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
topic Analysis of PDEs
35K70, 35H10, 35B65, 35B45, 35A23
url https://arxiv.org/abs/2401.12194