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.
ON THE APPROXIMATION OF THE PRINCIPAL EIGENVALUE FOR A CLASS OF NONLINEAR ELLIPTIC OPERATORS / Birindelli, Isabella; Camilli, Fabio; CAPUZZO DOLCETTA, Italo. - In: COMMUNICATIONS IN MATHEMATICAL SCIENCES. - ISSN 1539-6746. - STAMPA. - 15:(2017), pp. 55-75. [10.4310/CMS.2017.v15.n1.a3]
ON THE APPROXIMATION OF THE PRINCIPAL EIGENVALUE FOR A CLASS OF NONLINEAR ELLIPTIC OPERATORS
BIRINDELLI, Isabella;CAMILLI, FABIO;CAPUZZO DOLCETTA, Italo
2017
Abstract
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.| File | Dimensione | Formato | |
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