  Second order parabolic equations in Sobolev spaces with mixed norms are
studied. The leading coefficients (except $a^{11}$) are measurable in both time
and one spatial variable, and VMO in the other spatial variables. The
coefficient $a^{11}$ is measurable in time and VMO in the spatial variables.
The unique solvability of equations in the whole space is applied to solving
Dirichlet and oblique derivative problems for parabolic equations defined in a
half-space.
