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Concentration of
ground states in stationary mean-field games systems
Annalisa Cesaroni and Marco Cirant |
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Vol. 12 (2019), No. 3, 737–787
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Abstract |
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We provide the existence of classical solutions to stationary mean-field game systems in the whole space , with coercive potential and aggregating local coupling, under general conditions on the Hamiltonian. The only structural assumption we make is on the growth at infinity of the coupling term in terms of the growth of the Hamiltonian. This result is obtained using a variational approach based on the analysis of the nonconvex energy associated to the system. Finally, we show that in the vanishing viscosity limit, mass concentrates around the flattest minima of the potential. We also describe the asymptotic shape of the rescaled solutions in the vanishing viscosity limit, in particular proving the existence of ground states, i.e., classical solutions to mean-field game systems in the whole space without potential, and with aggregating coupling. |
Keywords
ergodic mean-field games, semiclassical limit,
concentration-compactness method, mass concentration,
elliptic systems, variational methods
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Mathematical Subject Classification 2010
Primary: 35J50
Secondary: 49N70, 35J47, 91A13, 35B25
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Milestones
Received: 16 August 2017
Revised: 25 May 2018
Accepted: 29 June 2018
Published: 7 October 2018
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Authors |
| Annalisa Cesaroni | |
| Dipartimento di Scienze
Statistiche Università di Padova Padova Italy |
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| Marco Cirant | |
| Dipartimento di Matematica “Tullio
Levi-Civita” Università di Padova Padova Italy |
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