Regularity results on the parabolic Monge–Ampère equation with VMO type data

This paper establishes interior estimates for LpLp-norms, Orlicz norms of solutions to the parabolic Monge–Ampère equation −utdetD2u=f(x,t) provided that f(x,t)f(x,t) is positive, bounded, and satisfies a VMO  -type condition, and some integrability conditions for ftft. Our results improve the corresponding results in Gutiérrez and Huang (2001) [8] in some sense.