Elliptic Equations Associated with Brownian Motion with Singular Drift

Abstract

In this paper, we first obtain the existence and uniqueness of solution u of elliptic equation associated with Brownian motion with singular drift. We then use the regularity of the weak solution u and the Zvonkin-type transformation to show that there is a unique weak solution to a stochastic differential equation when the drift is a measurable function.

Keywords

Elliptic equations / Zvonkin-type transformation / Weak solution / Singular drift

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