  The solvability in Sobolev spaces $W^{1,2}_p$ is proved for nondivergence
form second order parabolic equations for $p>2$ close to 2. The leading
coefficients are assumed to be measurable in the time variable and two
coordinates of space variables, and almost VMO (vanishing mean oscillation)
with respect to the other coordinates. This implies the $W^{2}_p$-solvability
for the same $p$ of nondivergence form elliptic equations with leading
coefficients measurable in two coordinates and VMO in the others. Under
slightly different assumptions, we also obtain the solvability results when
$p=2$.
