Gradient regularity and potential estimates for fractional drift--diffusion equations in the critical and subcritical ranges

Qi Xue, Chao Zhang

We establish scale-invariant interior $C^{1,\alpha }$ estimates for bounded viscosity solutions of $(-\Delta {)}^{s}u+b\cdot \nabla u=f$ for $s\in [1/2,1)$ with locally Hölder $b$ and $f$. The criti…