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

Abstract

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 thatwhere R is the largest radius of a ball included in the domain Ω ⊂ R n , and λ 1,p (Ω) and λ 1,∞ (Ω) are the principal eigenvalue for the homogeneous p-laplacian and the homogeneous infinity laplacian respectively.