A Zvonkin's transformation for stochastic differential equations with singular drift and applications - Chenggui Yuan (Journal of Differential Equations, 2021)
In this paper, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts by establishing the localized $L^p$-$L^q$ estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz first order term. The associated Krylov's estimate is established. As applications, dimension-free Harnack inequalities are established for stochastic equations with H\"older continuous diffusion coefficient and singular drift term without regularity assumption.