Abstract
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.
Funding Statement
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.
Acknowledgments
We thank the anonymous referees for their thoughtful comments which helped to improve our manuscript greatly.
Citation
Wilfrid Gangbo. Alpár R. Mészáros. Chenchen Mou. Jianfeng Zhang. "Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity." Ann. Probab. 50 (6) 2178 - 2217, November 2022. https://doi.org/10.1214/22-AOP1580
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