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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 vectorfields (containing vector fields having critical-order singularities), andcharacterize quantitative dependence of the $\mathcal W^{1+\frac{2}{q},p}$ ($2\leq p < q$) and the $C^{0,\gamma}$ regularity of solutions to thecorresponding elliptic equation in $L^p$ on the value of the form-bound of $b$.

$\mathcal W^{\alpha, p}$ and $C^{0,\gamma}$ regularity of solutions to $(\mu - \Delta + b \cdot \nabla)u=f$ with form-bounded vector fields