# Lyapunov type inequality for extremal Pucci's equations

## TL;DR

This paper derives a Lyapunov inequality for extremal Pucci's equations, extending classical results to fully nonlinear elliptic equations, which could impact stability analysis and eigenvalue estimates.

## Contribution

It introduces a Lyapunov type inequality for extremal Pucci's equations, generalizing classical inequalities to a broader class of nonlinear elliptic PDEs.

## Key findings

- Established Lyapunov inequality for extremal Pucci's equations
- Extended classical Lyapunov inequalities to fully nonlinear elliptic equations
- Provides tools for stability and eigenvalue analysis in nonlinear PDEs

## Abstract

In this article, we establish Lyapunov type inequality for the following extremal Pucci's equation \begin{equation*} \left\{ \begin{aligned}{} \mathcal{M}^{+}_{\lambda,\Lambda}(D^{2}u)+a(x)u&=0~\text{in}~\Omega,\\ u&=0~\text{on}~\partial\Omega, \end{aligned} \right. \end{equation*} where $\Omega$ is a smooth bounded domain in $\R^{N},~N\geq2$. This works generalize the well-known works on Lyapunov inequalities to fully nonlinear elliptic equations.