A complex parabolic type monge-ampère equation

Abstract

The complex parabolic type Monge-Ampere equation we are dealing with is of the form\((\partial u/\partial t){\text{ det[}}\partial ^2 u/\partial z_i {\text{ }}\partial \overline z _j ] = f\) inB × (0,T),u=ϕ on Γ, whereB is the unit ball in ℂd,d>1, and Γ is the parabolic boundary ofB × (0,T). Solutionu is proved unique in the class\(C(\bar B \times [0,T]) \cap W_{\infty ,loc}^{2,1} (B \times (0,T))\).