TY - JOUR
T1 - Existence for stationary mean-field games with congestion and quadratic Hamiltonians
AU - Gomes, Diogo A.
AU - Mitake, Hiroyoshi
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2015/9/3
Y1 - 2015/9/3
N2 - Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
AB - Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
UR - http://hdl.handle.net/10754/594122
UR - http://link.springer.com/10.1007/s00030-015-0349-7
UR - http://www.scopus.com/inward/record.url?scp=84945453305&partnerID=8YFLogxK
U2 - 10.1007/s00030-015-0349-7
DO - 10.1007/s00030-015-0349-7
M3 - Article
SN - 1021-9722
VL - 22
SP - 1897
EP - 1910
JO - Nonlinear Differential Equations and Applications NoDEA
JF - Nonlinear Differential Equations and Applications NoDEA
IS - 6
ER -