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

2021/11/27 by N. V. Krylov, Krylov, N. V.
Computer Science · Mathematics · #60H10 #60J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2111.13795

openalex publication_date 2021/11/27 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We consider Itô uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W¹_2+ε,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.

Related

• On strong solutions of Itô's equations with a ∈ W¹_d and b ∈ L_d
• On strong solutions of time inhomogeneous Itô's equations with Morrey diffusion and drift
• On strong solutions of time inhomogeneous Itô's equations with Morrey diffusion gradient and drift. A supercritical case
• Some properties of solutions of Itô equations with drift in L_d+1
• On strong solutions of time inhomogeneous Itô's equations with "supercritical" diffusion and drift