Existence of a solution to an equation arising from the theory of Mean Field Games
Existence of a solution to an equation arising from the theory of Mean Field Games
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DOI：
10.1016/j.jde.2015.08.001
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发表时间：
2015-12
影响因子：
2.4
通讯作者：
W. Gangbo;A. Swiech
中科院分区：
文献类型：
--
作者：
W. Gangbo;A. Swiech
本文构造了文献[48]中引入的非局部Hamilton-Jacobi方程（1.1）的小时间强解，即所谓的主方程，它起源于平均场博弈理论。我们发现了在[2]，[19]，[20]中研究的局部Hamilton-Jacobi方程的度量粘性解与（1.1）的解之间的联系。因此，我们恢复了在[48]中首次证明的一阶平均场对策方程（1.2）解的存在性，并在主方程（1.1）和平均场对策方程（1.2）之间建立了更严格的联系。
We construct a small time strong solution to a nonlocal Hamilton–Jacobi equation (1.1) introduced in [48], the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton–Jacobi equations studied in [2], [19], [20] and solutions to (1.1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved in [48], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2).