TY - JOUR
T1 - MEAN FIELD GAMES MASTER EQUATIONS WITH NONSEPARABLE HAMILTONIANS AND DISPLACEMENT MONOTONICITY
AU - Gangbo, By Wilfrid
AU - Mészáros, Alpár R.
AU - Mou, Chenchen
AU - Zhang, Jianfeng
N1 - KAUST Repository Item: Exported on 2022-12-07
Acknowledged KAUST grant number(s): ORA-2021-CRG10-4674.2
Acknowledgements: The research of WG was supported by NSF Grant DMS-1700202 and Air Force Grant FA9550-18-1-0502. ARM was partially supported by the King Abdullah University of Science and Technology Research Funding (KRF) under Award No. ORA-2021-CRG10-4674.2. CM gratefully acknowledges the support by CityU Start-up Grant 7200684 and Hong Kong RGC Grant ECS 9048215. The research of JZ was supported in part by NSF Grant DMS-1908665
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2022/11/1
Y1 - 2022/11/1
N2 - In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry–Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.
AB - In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry–Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.
UR - http://hdl.handle.net/10754/686249
UR - https://projecteuclid.org/journals/annals-of-probability/volume-50/issue-6/Mean-field-games-master-equations-with-nonseparable-Hamiltonians-and-displacement/10.1214/22-AOP1580.full
UR - http://www.scopus.com/inward/record.url?scp=85142293922&partnerID=8YFLogxK
U2 - 10.1214/22-AOP1580
DO - 10.1214/22-AOP1580
M3 - Article
SN - 2168-894X
VL - 50
SP - 2178
EP - 2217
JO - Annals of Probability
JF - Annals of Probability
IS - 6
ER -