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

We consider the operator $-\mathrm{\Delta }+b\cdot \mathrm{\nabla }$ 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 ${\mathcal{W}}^{1+\frac{2}{q},p}$ ($2 \leq p < q$)andthe$C^{0,\gamma}$ regularity of solutions to the corresponding elliptic equation in $L^p$ on the value of the form-bound of $b$.