40 citations · 72 across the 8 of their papers we have counts for
4 papers · 1 filter
Travelling waves for a Frenkel-Kontorova chain
Boris Buffoni, Hartmut Schwetlick, Johannes Zimmer
In this article, the Frenkel-Kontorova model for dislocation dynamics is considered, where the on-site potential consists of quadratic wells joined by small arcs, which can be spin…
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…
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…
Optimal mass transportation and Mather theory
Patrick Bernard, Boris Buffoni
We study optimal transportation of measures on compact manifolds for costs defined from convex Lagrangians. We prove that optimal transportation can be interpolated by measured Lip…