A generalization of the Hopf-Cole transformation for stationary Mean-Field Games systems

被引：9
|
作者：
Cirant, Marco [1 ]
机构：
[1] Univ Milan, Dipartimento Matemat F Enriques, I-20133 Milan, Italy
来源：
COMPTES RENDUS MATHEMATIQUE | 2015年 / 353卷 / 09期
关键词：
REGULARITY;
D O I：
10.1016/j.crma.2015.06.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note we propose a transformation that decouples stationary Mean-Field Games systems with superlinear Hamiltonians of the form vertical bar p vertical bar(r)', r' > 1, and turns the Hamilton-Jacobi-Bellman equation into a quasi-linear equation involving the r-Laplace operator. Such a transformation requires an assumption on solutions to the system, which is satisfied for example in space dimension one or if solutions are radial. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：807 / 811
页数：5
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