Geodesic
Time-periodic Evans approach to weak KAM theory
Minimax theory and its applications, Tome 3 (2018) no. 2
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We study the time-periodic version of Evans approach to weak KAM theory. Evans minimization problem is equivalent to a first order mean field game system. For the mechanical Hamiltonian we prove the existence of smooth solutions. We introduce the corresponding effective Lagrangian and Hamiltonian and prove that they are smooth. We also consider the limiting behavior of the effective Lagrangian and Hamiltonian, Mather measures and minimizers.
Mots-clés : Time-periodic weak KAM solution, effective Lagrangian and Hamiltonian, mean f ield game approximation 
@article{MTA_2018_3_2_a5,
     author = {H\'ector S\'anchez Morgado},
     title = {Time-periodic {Evans} approach to weak {KAM} theory},
     journal = {Minimax theory and its applications},
     year = {2018},
     volume = {3},
     number = {2},
     zbl = {1406.49045},
     url = {http://geodesic.mathdoc.fr/item/MTA_2018_3_2_a5/}
}
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Héctor Sánchez Morgado. Time-periodic Evans approach to weak KAM theory. Minimax theory and its applications, Tome 3 (2018) no. 2. http://geodesic.mathdoc.fr/item/MTA_2018_3_2_a5/