Abstract: For a class of more general elliptic Monge-Ampère operators raised by Caffarelli-Nirenberg-Spruck, the corresponding parabolic Monge-Ampère equation was studied, the existence and uniqueness of the classical solution to the first boundary-initial value problem for the equation were established, which extended a result of Monge-Ampère equation described by Ladyzhenskaya-Ivochkina.

Key words: more general form, fully nonlinear, non-uniformly parabolic, Monge-Ampère type equation