\(W^{2,p}\) estimates for the parabolic Monge-Ampère equation (Q5949562)

This paper is devoted to the parabolic Monge-Ampère operator \[ {\mathcal M}u= -u_t+\det D_x^2u, \] where \(u=u(t,x)\) is convex in \(x\in \mathbb{R}^n\) and nonincreasing in \(t\in R\), and \(D^2u=D_x^2u\) denotes the Hessian of \(u\) with respect to the variable \(x\). The goal of this paper is to show that solutions \(u\) to \({\mathcal M}u=f\) with \(f\) positive, continuous, and \(f_t\) satisfying certain growth conditions, have second derivatives in \(L^p\) for \(0<p< \infty\).