Strong Comparison Principle for p-harmonic functions in Carnot-Caratheodory spaces

2017/07/19 by Luca Capogna, Capogna, Luca, Xiaodan Zhou +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1707.06272

openalex publication_date 2017/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Bony's propagation of support argument \citeBony to C¹ solutions of the non-homogeneous sub-elliptic p-Laplacian associated to a system of smooth vector fields satisfying Hörmander's finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf \citeTolksdorf.

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