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We study the Dirichlet problem for a second order linear elliptic equation ina bounded smooth domain $\Omega$ in $\mathbb{R}^n$, $n \ge 3$, with the drift$\mathbf{b} $ belonging to the critical weak space $L^{n,\infty}(\Omega )$. Wedecompose the drift $\mathbf{b} = \mathbf{b}_1 + \mathbf{b}_2$ in which$\text{div} \mathbf{b}_1 \geq 0$ and $\mathbf{b}_2$ is small only in a smallscale quasi-norm of $L^{n,\infty}(\Omega )$. Under this new smallnesscondition, we prove existence, uniqueness, and regularity estimates of weaksolutions to the problem and its dual. H\"{o}lder regularity and derivativeestimates of weak solutions to the dual problem are also established. As aresult, we prove uniqueness of very weak solutions slightly below thethreshold. When $\mathbf{b}_2 =0$, our results recover those by Kim and Tsai in[SIAM J. Math. Anal. 52 (2020)]. Due to the new small scale quasi-norm, ourresults are new even when $\mathbf{b}_1=0$.

On linear elliptic equations with drift terms in critical weak spaces