The Third Initial-Boundary Value Problem for a Class of Parabolic Monge-Ampère Equations

Abstract

For the more general parabolic Monge-Ampère equations defined by the operator $F(D^2u + σ(x))$, the existence and uniqueness of the admissible solution to the third initial-boundary value problem for the equation are established. A new structure condition which is used to get a priori estimate is established.