多重积分Nash平衡点的Lipschitz估计

LIPSCHITZ ESTIMATES OF NASH EQUILIBRIA FOR VARIATIONAL INTEGRALS

设F（p，q）和G（p，q）在无穷远点的邻域内是分别关于p和q的近似凸函数，且具有二次增长．考虑由F和G构成的一对定义在Soblev空间中的泛函．本文利用blowup技巧，证明了这样一对泛函的Nash平衡点实际上是Lipschitz连续的．

We study a kind of coupled functionals defined in a vector-valued SobolevSpace by a function F(p, q) which is convex and has square growth in p and a function G(p, q)which is convex and has square growth in q. By the use of the blow-up technique, we provethat the Nash equilibrium for these coupled functionals is Lipschitz continuous.