Existence of a solution to an equation arising from the theory of Mean Field Games

被引：64

作者：

Gangbo, Wilfrid ^{[1
]}

Swiech, Andrzej ^{[1
]}

机构：

[1] Georgia Inst Technol, Atlanta, GA 30332 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 11期

基金：

美国国家科学基金会;

关键词：

NASH; PRINCIPLE; SYSTEMS;

D O I：

10.1016/j.jde.2015.08.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a small time strong solution to a nonlocal Hamilton Jacobi equation (1.1) introduced in [481, 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 148], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2). (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：6573 / 6643

页数：71