Strong Comparison Principles for Some Nonlinear Degenerate Elliptic Equations

TL;DR

This paper establishes strong comparison principles and Hopf Lemma for viscosity solutions of certain nonlinear degenerate elliptic equations, including the conformal Hessian operator, advancing theoretical understanding of these operators.

Contribution

It introduces new strong comparison principles and Hopf Lemma results for a class of nonlinear degenerate elliptic operators, including the conformal Hessian.

Findings

Proved strong comparison principle for viscosity solutions.

Established Hopf Lemma for the class of operators.

Applied results to the conformal Hessian operator.

Abstract

In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form $\nabla^2 \psi + L(x,\nabla \psi)$, including the conformal hessian operator.