中文摘要：

该文通过构造闸函数将整体约化到边界,证明了二维Monge-Ampère型方程Neumann边值问题解的二阶导数估计,进而得到该方程Neumann边值问题经典解的存在性以及正则性.

英文摘要：

In this paper,we prove the second order derivatives estimates of Monge-Ampère type equations with Neumann boundary condition,using the method of auxiliary function which reduce the global estimates to the boundary.Then,we obtain the existence and regularity of the classical solutions for the equations.