Non coercive unbounded first order Mean Field Games: The Heisenberg example

Paola Mannucci, Claudio Marchi, Nicoletta Tchou

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper we study evolutive first order Mean Field Games in the Heisenberg group; each agent can move in the whole space but it has to follow “horizontal” trajectories which are given in terms of the vector fields generating the group and the kinetic part of the cost depends only on the horizontal velocity. The Hamiltonian is not coercive in the gradient term and the coefficients of the first order term in the continuity equation may have a quadratic growth at infinity. The main results of this paper are two: the former is to establish the existence of a weak solution to the Mean Field Game systems while the latter is to represent this solution following the Lagrangian formulation of the Mean Field Games. We also provide some generalizations to Heisenberg-type structures.
Original languageEnglish (US)
Pages (from-to)809-840
Number of pages32
JournalJournal of Differential Equations
StatePublished - Dec 7 2021
Externally publishedYes

ASJC Scopus subject areas

  • Analysis


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