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In this paper we prove the stochastic homeomorphism flow property and thestrong Feller property for stochastic differential equations with sigular timedependent drifts and Sobolev diffusion coefficients. Moreover, the local wellposedness under local assumptions are also obtained. In particular, we extendKrylov and R\"ockner's results in \cite{Kr-Ro} to the case of non-constantdiffusion coefficients.

Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients