  The attracting inverse-square drift provides a prototypical counterexample to
solvability of singular SDEs: if the coefficient of the drift is larger than a
certain critical value, then no weak solution exists. We prove a positive
result on solvability of singular SDEs where this critical value is attained
from below (up to strict inequality) for the entire class of form-bounded
drifts. This class contains e.g. the inverse-square drift, the critical
Ladyzhenskaya-Prodi-Serrin class. The proof is based on a $L^p$ variant of De
Giorgi's method.
