English

The second boundary value problem for a discrete Monge-Ampere equation

Numerical Analysis 2024-07-11 v5 Numerical Analysis

Abstract

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 propose is the natural generalization of the popular Oliker-Prussner method proposed in 1988. For the discretization of the differential operator, we use a discrete analogue of the subdifferential. Existence, unicity and stability of the solutions to the discrete problem are established. Convergence results to the continuous problem are given.

Keywords

Cite

@article{arxiv.1910.14376,
  title  = {The second boundary value problem for a discrete Monge-Ampere equation},
  author = {Gerard Awanou},
  journal= {arXiv preprint arXiv:1910.14376},
  year   = {2024}
}
R2 v1 2026-06-23T12:00:38.445Z