  Recently Krylov established weak existence of solutions to SDEs for
integrable drifts in mixed Lebesgue spaces, whose exponents satisfy the
condition $1/q+d/p\leq 1$, thus going below the celebrated
Ladyzhenskaya-Prodi-Serrin condition. We present here a variant of such result,
whose proof relies on an alternative technique, based on a partial Zvonkin
transform; this allows for drifts with growth at infinity and/or in uniformly
local Lebesgue spaces.
