In this work we propose a natural discretization of the second boundary condition for the Monge-Ampere equation of geometric optics and optimal transport. It 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.

翻译：在这项工作中,我们建议对蒙古-阿曼等式的第二个边界条件进行自然分解,即几何光学和最佳运输,这是1988年提出的流行的奥立克-普鲁斯纳方法的自然普遍化,对于差分操作员的分解,我们使用分解操作员的离散类比,确定了离散问题解决办法的存在、一致性和稳定性,对持续问题得出了一致的结果。