Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity
Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity
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DOI：
10.1214/22-aop1580
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发表时间：
2021-01
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影响因子：
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通讯作者：
W. Gangbo;A. M'esz'aros;Chenchen Mou;Jianfeng Zhang
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文献类型：
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作者：
W. Gangbo;A. M'esz'aros;Chenchen Mou;Jianfeng Zhang
。在这篇手稿中，我们提出了不可分离哈密顿量的结构条件，我们将其称为位移单调性条件，以研究二阶平均场博弈主方程。基于对测量变量解的先验均匀 Lipschitz 估计，双线性形式的耗散率被引入全局（及时）适定性理论。位移单调性有时与广泛使用的 Lasry-Lions 单调性条件成二分法，即使仅限于可分离的哈密顿量，这项工作的新颖性仍然存在。
. In this manuscript, we propose a structural condition on non-separable 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.