Existence for stationary mean-field games with congestion and quadratic Hamiltonians

被引：30

作者：

Gomes, Diogo A. ^{[1
,2
]}

Mitake, Hiroyoshi ^{[3
]}

机构：

[1] King Abdullah Univ Sci & Technol, CSMSE Div, Thuwal 239556900, Saudi Arabia

[2] KAUST SRI Uncertainty Quantificat Ctr Computat Sc, Thuwal, Saudi Arabia

[3] Hiroshima Univ, Inst Sustainable Sci & Dev, Higashihiroshima 7398527, Japan

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2015年 / 22卷 / 06期

关键词：

Mean-field games; Quadratic Hamiltonians; Congestion;

D O I：

10.1007/s00030-015-0349-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions.

引用

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页码：1897 / 1910

页数：14

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