English

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 C1C^1 solutions of the non-homogeneous sub-elliptic pp-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}
}