ON THE APPROXIMATION OF THE PRINCIPAL EIGENVALUE FOR A CLASS OF NONLINEAR ELLIPTIC OPERATORS

We present a nite difference method to compute the principal eigenvalue and the corresponding eigenfunction for a large class of second order elliptic operators including notably linear operators in non divergence form and fully nonlinear operators. The principal eigenvalue is computed by solving a nite-dimensional nonlinear min-max optimization problem. We prove the convergence of the method and we discuss its implementation. Some examples where the exact solution is explicitly known show the effectiveness of the method