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Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation
Brittany D. Froese, Adam M. Oberman
The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, ela…
The Dirichlet problem for the convex envelope
Luis Silvestre, Adam M. Oberman
The Convex Envelope of a given function was recently characterized as the solution of a fully nonlinear Partial Differential Equation (PDE). In this article we study a modified pro…
Anisotropic Total Variation Regularized L^1-Approximation and Denoising/Deblurring of 2D Bar Codes
Rustum Choksi, Yves van Gennip, Adam Oberman
We consider variations of the Rudin-Osher-Fatemi functional which are particularly well-suited to denoising and deblurring of 2D bar codes. These functionals consist of an anisotro…
Convergent finite difference solvers for viscosity solutions of the elliptic Monge-Ampère equation in dimensions two and higher
Brittany D. Froese, Adam M. Oberman
The elliptic Monge-Ampère equation is a fully nonlinear Partial Differential Equation that originated in geometric surface theory and has been applied in dynamic meteorology, elast…