On strong solutions of Itô's equations with $Dσ$ and $b$ in Morrey classes containing $L_{d}$

We consider Itô uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W^{1}_{2+\varepsilon,loc}$, 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.

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