We extend Bony’s propagation of support argument to C1 solutions of the non-homogeneous sub-elliptic p−Laplacian associated to a system of smooth vector fields satisfying Hormander’s finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf.
Capogna, L., & Zhou, X. (2017). Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces. Retrieved from https://digitalcommons.wpi.edu/mathematicalsciences-pubs/73