A LOWER BOUND FOR THE PRINCIPAL EIGENVALUE OF FULLY NONLINEAR ELLIPTIC OPERATORS

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 lim(p ->infinity) lambda(1,p) (Omega) = lambda(1,infinity) (Omega) = (pi/2R)(2) where R is the largest radius of a ball included in the domain Omega subset of R-n, and lambda(1,p) (Omega) and lambda(1,infinity) (Omega) are the principal eigenvalue for the homogeneous p-laplacian and the homogeneous infinity laplacian respectively.