The First Boundary Value Problem for General Parabolic Monge-Ampere Equation (Journal of Partial Differential Equations, 1990)
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 = &#966(x, t) on &#8706, Q It is proved that there exists a unique convex in x solution to the problem from C^{1+&#946,2+&#946/2}(\overline{Q}) under certain structure aod smoothness conditions (H3) - (H7).
Keywords: General parabolic Mange-Ampere equation; first boundary value problem; classical solution