Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators

2024/01/22 by Francesca Anceschi, Helge Dietert, Anceschi, Francesca +9 · 1 citation
Mathematics · #35A23 #35B45 #35B65 #35H10 #35K70 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2401.12194

openalex publication_date 2024/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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