In this paper, 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, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts. The associated Krylov's estimate is established. As applications, dimension-free Harnack inequalities are established for stochastic equations with Hölder continuous diffusion coefficient and singular drift term without regularity assumption.

中文翻译：

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奇异漂移随机微分方程的Zvonkin变换及其应用

在本文中，通过建立本地化 ${升}^{磷}$——${升}^q$对于具有奇异一阶项和 Lipschitz 一阶项的抛物线偏微分方程的估计和 Sobolev 估计，给出了具有奇异和 Lipschitz 漂移的随机微分方程的新 Zvonkin 型变换。建立关联的 Krylov 估计。作为应用，我们建立了具有 Hölder 连续扩散系数和奇异漂移项的随机方程的无量纲 Harnack 不等式，没有正则假设。