The Dirichlet Problem for elliptic equations with singular drift terms

We establish $L^p$ solvability of the Dirichlet problem, for some finite $p$, in a 1-sided chord-arc domain $Ω$ (i.e., a uniform domain with Ahlfors-David regular boundary), for elliptic equations of the form \[ Lu=-\text{div}(A\nabla u) + {\bf B}\cdot \nabla u=:L_0 u+ {\bf B}\cdot \nabla u=0, \] gi