Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian. (English) Zbl 1145.65085
Summary: Certain fully nonlinear elliptic partial differential equations can be written as functions of the eigenvalues of the Hessian. These include: the Monge-Ampère equation, Pucci’s maximal and minimal equations, and the equation for the convex envelope. In this article we build convergent monotone finite difference schemes for the aforementioned equations. Numerical results are presented.
MSC:
65N06 | Finite difference methods for boundary value problems involving PDEs |
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
35R35 | Free boundary problems for PDEs |
35J65 | Nonlinear boundary value problems for linear elliptic equations |
49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |