On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators

2014/04/01 by Alessia E. Kogoj, Kogoj, Alessia E., Y. Pinchover +5 · 1 citation
Mathematics · #35B53 #35K15 #35K65 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary: 35K70 #Secondary: 35B09 #math.AP #math.FA #msc:35B09 #msc:35B53 #msc:35K15 #msc:35K65 #msc:35K70

paper · pdf · doi:10.48550/arxiv.1404.0288

The results of the present version recover most of the ones in the previous version, but, on top of it, this new version contains some further new and interesting results

openalex publication_date 2014/04/01 · arxiv created 2015/11/16 · arxiv updated 2015/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note contains a representation formula for positive solutions of linear degenerate second-order equations of the form ∂_t u (x,t) = ∑_j=1^m X_j² u(x,t) + X₀ u(x,t) (x,t) ∈ ℝ^N × ]- ∞ ,T[, proved by a functional analytic approach based on Choquet theory. As a consequence, we obtain Liouville-type theorems and uniqueness results for the positive Cauchy problem.

Citations

• Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators
• Harnack inequality for hypoelliptic second order partial differential operators

Cited by

• Harnack inequality for Bessel operators

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