On strong solutions of Itô’s equations with Dσ and b in Morrey classes containing Ld

Abstract

We consider Itô uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in ${\mathit{W}}_{2+\mathit{\epsilon },\mathrm{loc}}^1$, and the drift in a Morrey class containing ${\mathit{L}}_{\mathit{d}}$. 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.