PARABOLIC EQUATIONS IN SIMPLE CONVEX POLYTOPES WITH TIME IRREGULAR COEFFICIENTS

We prove the W-p(1,2)-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when p is an element of (1, 2]. We also consider the corresponding Neumann problem in a half space when p is an element of [2, infinity). Similar results are obtained for equations in a half space with coefficients which are measurable in a tangential direction and have small mean oscillations in the other directions. Equations with discontinuous coefficients in nonsmooth domains emerge from problems in mechanics, engineering, and biology, to name a few fields.