$L_p$-estimates of the conormal derivative problem for parabolic equations with time measurable coefficients and $A_p$-weights

Abstract

This paper investigates weighted mixed-norm estimates for divergence-type parabolic equations on Reifenberg-flat domains with the conormal derivative boundary condition. The leading coefficients are assumed to be merely measurable in the time variable and to have small mean oscillations in the spatial variables. In deriving the boundary estimates, we overcome a regularity issue by employing half-time derivative estimates.