Strong Comparison Principle for p-Harmonic Functions in Carnot-Caratheodory Spaces

Authors

Luca Capogna, Worcester Polytechnic InstituteFollow
Xiaodan Zhou, Worcester Polytechnic Institute

Document Type

Article

Publication Date

1-1-2018

Publication Title

Proceedings of the American Mathematical Society

Abstract

We extend Bony’s propagation of support argument to C1 solutions of the nonhomogeneous subelliptic 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.

Keywords

P-harmonic functions, Strong comparison principle, Sub-Riemannian geometry, Subelliptic PDE

Volume

146

Issue

10

First Page

4265

Last Page

4274

DOI

10.1090/proc/14113

ISSN

00029939

Comments

Author’s submitted manuscript.

Recommended Citation

Capogna, Luca and Zhou, Xiaodan, "Strong Comparison Principle for p-Harmonic Functions in Carnot-Caratheodory Spaces" (2018). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/127