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July  2008, 10(1): 221-238. doi: 10.3934/dcdsb.2008.10.221

Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian

Adam M. Oberman 1,

1. 

Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

Received  June 2007 Revised  December 2007 Published  April 2008

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.
Keywords: partial differential equations, convex functions, viscosity solutions, Monge-Ampère equation, convex hull., Pucci maximal equation, finite difference schemes.
Mathematics Subject Classification: 65N06, 65N12, 65M06, 65M12, 35B50, 35J60, 35R35, 35K65, 49L2.
Citation: Adam M. Oberman. Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 221-238. doi: 10.3934/dcdsb.2008.10.221
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