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The well-posedness for SDEs with singularity in both space and distributionvariables is derived, where the drift is bounded and Lipschitz continuous underweighted variation distance and the diffusion is allowed to be Lipschitzcontinuous under $L^\eta$($\eta\in(0,1]$)-Wasserstein distance. Moreover, theregularity estimate is established when the drift is bounded and Lipschitzcontinuous under total variation distance.

McKean-Vlasov SDEs with Sigularity in Distribution Variable and Distribution Dependent Diffusion