The First Boundary Value Problem for General Parabolic Monge-Ampere Equation

In this note we consider the first boundary value problem for a general parabolic Monge-Ampere equation u_t - log det(D_{ij}u) = f(x, t, u,D_2u) in Q, quad u = φ(x, t) on ∂, Q It is proved that there exists a unique convex in x solution to the problem from C^{1+β,2+β/2}(overline{Q}) under certain structure aod smoothness conditions (H3) - (H7).