C1,α REGULARITY OF SOLUTIONS TO PARABOLIC MONGE-AMPERE EQUATIONS

We study interior C-1,C-alpha regularity of viscosity solutions of the parabolic Monge-Ampere equation u(t) = b(x,t) (detD(2)u)(p), with exponent p> 0 and with coefficients b which are bounded and measurable. We show that when p is less than the critical power 1/n-2 then solutions become instantly C-1,C-alpha in the interior. Also, we prove the same result for any power p > 0 at those points where either the solution separates from the initial data, or where the initial data is C-1,C-beta.