  We consider the operator $-\Delta +b \cdot \nabla$ with $b:\mathbb R^d
\rightarrow \mathbb R^d$ ($d \geq 3$) in the class of form-bounded vector
fields (containing vector fields having critical-order singularities), and
characterize quantitative dependence of the $\mathcal W^{1+\frac{2}{q},p}$ ($2
\leq p < q$) and the $C^{0,\gamma}$ regularity of solutions to the
corresponding elliptic equation in $L^p$ on the value of the form-bound of $b$.
