2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121936We 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.Dynamical SystemsOptimization and Control49Q20, 37J50, 35F20text