Strong comparison principle for 𝑝-harmonic functions in Carnot-Caratheodory spaces

Abstract

We extend Bony’s propagation of support argument to C 1 C^1 solutions of the nonhomogeneous subelliptic p 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.