  We consider an oblique derivative problem for non-divergence parabolic
equations with discontinuous in $t$ coefficients in a half-space. We obtain
weighted coercive estimates of solutions in anisotropic Sobolev spaces. We also
give an application of this result to linear parabolic equations in a bounded
domain. In particular, if the boundary is of class ${\cal C}^{1,\delta}$,
$\delta\in (0,1]$, then we present a coercive estimate of solutions in weighted
anisotropic Sobolev spaces, where the weight is a power of the distance to the
boundary.
