Title: On some properties of weak solutions to elliptic equations with divergence-free drifts,
Abstract: We discuss the local properties of weak solutions to the equation $-\Delta u
+ b\cdot\nabla u=0$. The corresponding theory is well-known in the case $b\in
L_n$, where $n$ is the dimension of the space. Our main interest is focused on
the case $b\in L_2$. In this case the structure assumption $\operatorname{div}
b=0$ turns out to be crucial.