Parabolic equations and SDEs with time-inhomogeneous Morrey drift

2023/01/31 by Kinzebulatov, D. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2301.13805

Abstract

We prove the unique weak solvability of stochastic differential equations with time-inhomogeneous drift in essentially the largest (scaling-invariant) Morrey class, i.e. with integrability parameter q>1 close to 1. The constructed weak solutions constitute a Feller evolution family. The proofs are based on a detailed Sobolev regularity theory of the corresponding parabolic equation.

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