The Pluripotential Cauchy-Dirichlet problem for complex Monge-Ampère flows

We develop the first steps of a parabolic pluripotential theory in bounded strongly pseudo-convex domains Cn. study certain degenerate complex Monge-Ampere equations, modelled on Kahler-Ricci flow evolving algebraic varieties with Kawamata log-terminal singularities. Under natural assumptions Cauchy-Dirichlet boundary data, we show that envelope subsolutions is semi-concave time and continuous space, provides unique solution such regularity.