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

10/31/2019

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by   Gerard Awanou, et al.

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In this work we propose a natural discretization of the second boundary condition for the Monge-Ampere equation of geometric optics and optimal transport. For the discretization of the differential operator, we use a recently proposed scheme which is based on a partial discrete analogue of a symmetrization of the subdifferential. Existence, unicity and stability of the solutions to the discrete problem are established. Convergence results to the continuous problem are given.