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

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