Lyapunov type inequality for extremal Pucci's equations

Abstract

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