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arXiv:1904.13287 [math.AP]AbstractReferencesReviewsResources

Weak KAM theory for potential MFG

Pierre Cardaliaguet, Marco Masoero

Published 2019-04-30Version 1

We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to infinity, of the value function of an optimal control problem stated in the space of measures. In addition, we show a mean field limit for the ergodic constant associated with the corresponding Hamilton-Jacobi equation.

Categories: math.AP, math.DS
Subjects: 49J20, 37K55, 37A99
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