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math.DS2005
Weak KAM pairs and Monge-Kantorovich duality
Patrick Bernard, Boris Buffoni
The dynamics of globally minimizing orbits of Lagrangian systems can be studied using the Barrier function, as Mather first did, or using the pairs of weak KAM solutions introduced…
math.DS2005
The Monge problem for supercritical Mane potentials on compact manifolds
Patrick Bernard, Boris Buffoni
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…