A-priori estimates for stationary mean-field games
A-priori estimates for stationary mean-field games
复制标题
固定平均场博弈的先验估计
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
H. Sánchez
中科院分区：
文献类型：
--
作者：
D. Gomes;G. E. Pires;H. Sánchez
本文建立了一类具有拟变分结构的平稳平均场对策的先验估计。
In this paper we establish a new class of a-priori estimates for stationary mean-field games which have a quasi-variational structure.
In particular we prove $W^{1,2}$ estimates for the value function $u$ and that the players distribution $m$ satisfies $sqrt{m}in W^{1,2}$.
We discuss further results for power-like nonlinearities and prove higher regularity if the space dimension is 2. In particular we also
obtain in this last case $W^{2,p}$ estimates for $u$.