一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题

The initial and Neumann boundary value problem for a class of parabolic Monge-Ampère equations

证明了一类抛物型Monge-Ampère方程具Neumann边界条件的初边值问题的古典解的存在惟一性。用比较原理证明了该问题至多存在一个古典解。在一定条件下,通过构造辅助函数和闸函数,得到严格凸解的先验估计结果,进而利用连续性方法得到了该问题严格凸解的存在性。

It is proved that the classical solution to the initial and Neumann boundary value problem for parabolic-type Monge-Ampère equations is existent and unique.Using the comparison principle,the uniqueness of the classical solution is shown.By employing proper auxiliary functions and barrier functions,the priori estimations are obtained.The existence of the strict convex classical solution is obtained by the continuous method.