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We consider It\^o uniformly nondegenerate equations with time independentcoefficients, the diffusion coefficient in $W^{1}_{d,loc}$, and the drift in$L_{d}$. We prove the unique strong solvability for any starting point andprove that as a function of the starting point the solutions are H\"oldercontinuous with any exponent $<1$. We also prove that if we are given asequence of coefficients converging in an appropriate sense to the originalones, then the solutions of approximating equations converge to the solution ofthe original one.

On strong solutions of It\^o's equations with a$\,\in W^{1}_{d}$ and b$\,\in L_{d}$