Comparison principles for some fully nonlinear subelliptic equations on the Heisenberg group

TL;DR

This paper establishes a strong comparison principle for a class of fully nonlinear subelliptic equations on the Heisenberg group, including CR invariant operators, advancing understanding of their solutions.

Contribution

It introduces a new strong comparison principle for nonlinear subelliptic operators on the Heisenberg group, encompassing CR invariant operators.

Findings

Proves a strong comparison principle for fully nonlinear subelliptic equations.

Includes CR invariant operators within the class of operators considered.

Provides theoretical foundation for uniqueness and stability of solutions.

Abstract

In this paper, we prove a form of the strong comparison principle for a class of fully nonlinear subelliptic operators of the form $\nabla^{2}_{H}\psi+L(\cdot,\psi,\nabla_{H}\psi)$ on the Heisenberg group, which include the CR invariant operators.