Ricerc@Sapienza

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.