  We consider the Dirichlet problem for a class of elliptic and parabolic
equations in the upper-half space $\mathbb{R}^d_+$, where the coefficients are
the product of $x_d^\alpha, \alpha \in (-\infty, 1),$ and a bounded uniformly
elliptic matrix of coefficients. Thus, the coefficients are singular or
degenerate near the boundary $\{x_d =0\}$ and they may not locally integrable.
The novelty of the work is that we find proper weights under which the
existence, uniqueness, and regularity of solutions in Sobolev spaces are
established. These results appear to be the first of their kind and are new
even if the coefficients are constant. They are also readily extended to
systems of equations.
