On a constant rank theorem for nonlinear elliptic PDEs

TL;DR

This paper presents a novel proof of a constant rank theorem for nonlinear elliptic PDEs, utilizing a linear eigenvalue expression instead of traditional symmetric function quotients.

Contribution

The authors introduce a new proof technique for the constant rank theorem, simplifying the approach by focusing on linear eigenvalue expressions.

Findings

New proof of Bian-Guan's constant rank theorem

Simplification of proof using linear eigenvalue expressions

Potential for broader application in nonlinear elliptic PDE analysis

Abstract

We give a new proof of Bian-Guan's constant rank theorem for nonlinear elliptic equations. Our approach is to use a linear expression of the eigenvalues of the Hessian instead of quotients of elementary symmetric functions.