212 citations · 505 across the 22 of their papers we have counts for
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Convergence of a damped Newton's method for discrete Monge-Ampere functions with a prescribed asymptotic cone
Gerard Awanou
For finite difference discretizations with linear complexity and provably convergent to weak solutions of the second boundary value problem for the Monge-Ampère equation, we give t…
The second boundary value problem for a discrete Monge-Ampere equation
Gerard Awanou
In this work we propose a discretization of the second boundary condition for the Monge-Ampere equation arising in geometric optics and optimal transport. The discretization we pro…
On weak convergence of Monge-Ampere measures for discrete convex mesh functions
Gerard Awanou
To a mesh function we associate the natural analogue of the Monge-Ampere measure. The latter is shown to be equivalent to the Monge-Ampere measure of the convex envelope. We prove…
Uniform limit of discrete convex functions
Gerard Awanou
We consider mesh functions which are discrete convex in the sense that their central second order directional derivatives are positive. Analogous to the case of a uniformly bounded…