Abstract:

It is proved that  a classical solution to the initial and Neumann boundary value problem for parabolic-type Monge-Ampère equation is existent and unique. Using compare principle, it is shown the uniqueness of the classical solution. 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.

Key words: Monge-Ampère equation; Neumann boundary condition; priori estimation