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

N. V. Krylov

paper

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

arXiv:2111.13795

Abstract

We consider Itô uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W_{2 + ε, l oc}^{1}$ , 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.

24 pages. An important example added. arXiv admin note: text overlap with arXiv:2007.06040

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

Abstract

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