Communications in Mathematical Sciences

Volume 15 (2017)

Number 1

On the approximation of the principal eigenvalue for a class of nonlinear elliptic operators

Pages: 55 – 75

DOI: http://dx.doi.org/10.4310/CMS.2017.v15.n1.a3

Authors

Isabeau Birindelli (Dip. di Matematica, “Sapienza” Università di Roma, Italy)

Fabio Camilli (Dip. di Scienze di Base e Applicate per l’Ingegneria, “Sapienza” Università di Roma, Italy)

Italo Capuzzo Dolcetta (Dip. di Matematica, “Sapienza” Università di Roma, Italy)

Abstract

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.

Keywords

principal eigenvalue, nonlinear elliptic operators, finite difference schemes, convergence

2010 Mathematics Subject Classification

35J60, 35P30, 65M06

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