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2019 Concentration of ground states in stationary mean-field games systems
Annalisa Cesaroni, Marco Cirant
Anal. PDE 12(3): 737-787 (2019). DOI: 10.2140/apde.2019.12.737

Abstract

We provide the existence of classical solutions to stationary mean-field game systems in the whole space  N , 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.

Citation

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Annalisa Cesaroni. Marco Cirant. "Concentration of ground states in stationary mean-field games systems." Anal. PDE 12 (3) 737 - 787, 2019. https://doi.org/10.2140/apde.2019.12.737

Information

Received: 16 August 2017; Revised: 25 May 2018; Accepted: 29 June 2018; Published: 2019
First available in Project Euclid: 25 October 2018

zbMATH: 06986452
MathSciNet: MR3864209
Digital Object Identifier: 10.2140/apde.2019.12.737

Subjects:
Primary: 35J50
Secondary: 35B25, 35J47, 49N70, 91A13

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 3 • 2019
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