The Monge problem for supercritical Mane potentials on compact manifolds
Dynamical Systems
2007-05-23 v2 Optimization and Control
Abstract
We prove the existence of an optimal map for the Monge problem when the cost is a supercritical Mane potential on a compact manifold. Supercritical Mane potentials form a class of costs which generalize the Riemannian distances. We describe new links between this transportation problem and viscosity subsolutions of the Hamilton-Jacobi equation.
Keywords
Cite
@article{arxiv.math/0502136,
title = {The Monge problem for supercritical Mane potentials on compact manifolds},
author = {Patrick Bernard and Boris Buffoni},
journal= {arXiv preprint arXiv:math/0502136},
year = {2007}
}