On strong solutions of It\^o's equations with $D\sigma$ and $b$ in Morrey classes containing $L_d$

We consider It^o uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W_{2+\epsilon ,loc}^1$, and the drift in a Morrey class containing $L_d$. We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.