Upper bounds for the eigenvalues of Hessian equations

TL;DR

This paper establishes upper bounds for the Dirichlet eigenvalues associated with a class of fully nonlinear elliptic Hessian equations, contributing to the understanding of their spectral properties.

Contribution

It provides new upper bounds for eigenvalues of Hessian equations, advancing spectral theory for nonlinear elliptic PDEs.

Findings

Derived explicit upper bounds for eigenvalues

Extended spectral analysis to fully nonlinear Hessian equations

Enhanced understanding of eigenvalue estimates in nonlinear PDEs

Abstract

We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equations