Conormal Problem of Higher-order Parabolic Systems with Time Irregular Coefficients

The paper is a comprehensive study of Lp and Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients on a half space and cylindrical domains with the conormal derivative boundary conditions. For the Lp estimates, we assume that the leading coefficients are only bounded and measurable in the t variable and have vanishing mean oscillations (VMOx) with respect to x. We also prove the Schauder estimates in two situations: the coefficients are Hölder continuous only in the x variable; the coefficients are Hölder continuous in the t variable as well on the lateral boundary.