Orlicz regularity for higher order parabolic equations in divergence form with coefficients in weak BMO

Abstract

We consider higher order parabolic equations in divergence form with measurable coefficients to find optimal regularity in Orlicz spaces of the maximum order derivatives of the weak solutions. The relevant minimal regularity requirement on the tensor matrix coefficients is of small BMO in the spatial variable and is measurable in the time variable. As a consequence we prove the classical W m,p regularity, m = 1, 2, . . . , 1 < p < ∞, for such higher order equations. In the same spirit the results easily extend to higher order parabolic systems as well as up to the boundary.