  We study the divergence form second-order elliptic equations with mixed
Dirichlet-conormal boundary conditions. The unique $W^{1,p}$ solvability is
obtained with $p$ being in the optimal range $(4/3,4)$. The leading
coefficients are assumed to have small mean oscillations and the boundary of
domain is Reifenberg flat. We also assume that the two boundary conditions are
separated by some Reifenberg flat set of co-dimension $2$ on the boundary.
