  We study both divergence and non-divergence form parabolic and elliptic
equations in the half space $\{x_d>0\}$ whose coefficients are the product of
$x_d^\alpha$ and uniformly nondegenerate bounded measurable matrix-valued
functions, where $\alpha \in (-1, \infty)$. As such, the coefficients are
singular or degenerate near the boundary of the half space. For equations with
the conormal or Neumann boundary condition, we prove the existence, uniqueness,
and regularity of solutions in weighted Sobolev spaces and mixed-norm weighted
Sobolev spaces when the coefficients are only measurable in the $x_d$ direction
and have small mean oscillation in the other directions in small cylinders. Our
results are new even in the special case when the coefficients are constants,
and they are reduced to the classical results when $\alpha =0$
