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We consider an oblique derivative problem for non-divergence parabolicequations with discontinuous in $t$ coefficients in a half-space. We obtainweighted coercive estimates of solutions in anisotropic Sobolev spaces. We alsogive an application of this result to linear parabolic equations in a boundeddomain. 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 weightedanisotropic Sobolev spaces, where the weight is a power of the distance to theboundary.

Oblique derivative problem for non-divergence parabolic equations with discontinuous in time coefficients