A Complex Parabolic Type Monge—Ampère Equation

摘要

The complex parabolic type Monge—Ampère equation we are dealing with is of the form (au/at)det [a~2 u/a z_i,az_j] = f in BX(0,T), u=Ψ on Γ, where B is the unit ball in C~d, d>1 , and o is the parabolic boundary of BX(0,T) . Solution u is proved unique in the class C(BX[0,T])∩ W~(2,1)_∞loc(BX(0,T)).