A complex parabolic type Monge-Ampère equation (Q678105)

This paper deals with the complex parabolic type Monge-Ampère equation \[ (\partial u/\partial t)+\text{det}[\partial^2u/\partial z_i\partial\overline z_j]=f\quad\text{in }B\times(0,T) \] with the boundary condition on the boundary of \(B\times(0,T)\), where \(B\) is the ball in \(\mathbb{C}^d\). Applying stochastic optimal control techniques associated with Monge-Ampère equation and using various evaluations, the author obtained the unique continuous solution in \(W^{1,2}_{\infty,\text{loc}}\).