  We consider the Dirichlet problems for second-order elliptic equations with
singular drifts given by $\mathbf{b}$. When the leading coefficients $A$ have
small mean oscillations in small balls and $\mathrm{div}\, A ,\mathbf{b}$ are
in $L^{2}$, we obtain $W^{1,p}$-results on bounded Lipschitz domains in
$\mathbb{R}^2$ with small Lipschitz constants.
