Regularity results on the parabolic Monge-Ampère equation with \(VMO\) type data
The author studies the interior regularity of weak solutions to the parabolic Monge-Ampère equation \[ -u_t \text{det}D^2u=f(x,t)\quad \text{ in } Q=\Omega\times (0,T] \] where \(u\) is a parabolic convex in \(Q\) and \(f\) is positive, bounded, satisfies a VMO-type condition, and some integrability conditions for \(f_t.\) There are obtained estimates for the \(L^p\)-norms and the Orlicz norms of solutions.
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