Convex-monotone functions and generalized solution of parabolic Monge–Ampère equation

In this paper, we study the generalized solution of the first initial boundary value problem for the parabolic Monge–Ampère equation −ut det D2u=f(x,t) in Q=Ω×(0,T], u= (x,t) on ∂pQ. We first get the Hölder continuity of the generalized solution in t, and then obtain the generalized solution in case f(x,t)=0, which improve the assumptions in the existence of generalized solution in (J. Partial Differential Equations 14(2) (2001) 149).