Communications in Mathematical Sciences
Volume 15 (2017)
On the approximation of the principal eigenvalue for a class of nonlinear elliptic operators
Pages: 55 – 75
We present a finite 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 finite-dimensional nonlinear min-max optimization problem. We prove the convergence of the method and discuss its implementation. Some examples where the exact solution is explicitly known show the effectiveness of the method.
principal eigenvalue, nonlinear elliptic operators, finite difference schemes, convergence
2010 Mathematics Subject Classification
35J60, 35P30, 65M06