Minimax Theory and its Applications 03 (2018), No. 2, 313--322
Copyright Heldermann Verlag 2018
Time-Periodic Evans Approach to Weak KAM Theory
Héctor Sánchez Morgado
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Cd. de México 04510, México
hector@matem.unam.mx
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.
Keywords: Time-periodic weak KAM solution, effective Lagrangian and Hamiltonian, mean field game approximation.
MSC: 49L99, 37J50, 35J62.
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