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In this article we present a new technique to obtain a lower bound for the principal Dirichlet eigenvalue of a fully nonlinear elliptic operator. We illustrate the construction of an appropriate radial function required to obtain the bound in several examples. In particular we use our results to prove that\begin{document}$   \lim_{p\to \infty}\lambda_{1,p}(\Omega) = \lambda_{1,\infty}(\Omega) = \left(\frac{\pi}{2R}\right)^2   $\end{document}where   \begin{document}$ R $\end{document}   is the largest radius of a ball included in the domain   \begin{document}$ \Omega\subset {\mathbb R}^n $\end{document}  , and   \begin{document}$ \lambda_{1,p}(\Omega) $\end{document}   and   \begin{document}$ \lambda_{1,\infty}(\Omega) $\end{document}   are the principal eigenvalue for the homogeneous   \begin{document}$ p $\end{document}  -laplacian and the homogeneous infinity laplacian respectively.

A lower bound for the principal eigenvalue of fully nonlinear elliptic operators