Zvonkin’s transform and the regularity of solutions to double divergence form elliptic equations

We study qualitative properties of solutions to double divergence form elliptic equations (or stationary Kolmogorov equations) on Rd. It is shown that the Harnack inequality holds for nonnegative if diffusion matrix A nondegenerate and satisfies Dini mean oscillation condition drift coefficient b locally integrable some power p > d. establish new estimates Lp-norms obtain a generalization known theorem Hasminskii existence probability solution equation case where Dini’s or belongs class VMO. These results are based analytic version Zvonkin’s transform coefficient.