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

A note on weak existence for singular SDEs