Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces
Analysis of PDEs
2017-07-21 v1 Differential Geometry
Metric Geometry
Abstract
We extend Bony's propagation of support argument \cite{Bony} to solutions of the non-homogeneous sub-elliptic Laplacian associated to a system of smooth vector fields satisfying H\"ormander's finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf \cite{Tolksdorf}.
Keywords
Cite
@article{arxiv.1707.06272,
title = {Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces},
author = {Luca Capogna and Xiaodan Zhou},
journal= {arXiv preprint arXiv:1707.06272},
year = {2017}
}