W2,p Estimates for the Parabolic¶Monge-Ampère Equation

Abstract

When u is a solution to the equation −u _t det D _x ² u=f with f positive, continuous, and f _t satisfying certain growth conditions, we establish estimates in L ^∞ for u _t and show that D _x ² u satisfies uniform interior estimates in L ^p for 0<p<∞.