  By using Zvonkin's transformation and a two-step fixed point argument in
distributions, the well-posedness and regularity estimates are derived for
singular McKean-Vlasov SDEs with distribution dependent noise, where the drift
contains a term growing linearly in space and distribution and a locally
integrable term independent of distribution, while the noise coefficient is
weakly differentiable in space and Lipschitz continuous in distribution with
respect to the sum of Wasserstein and weighted variation distances. The main
results extend existing ones derived for noise coefficients either independent
of distribution, or having nice linear functional derivatives in distribution.
Singular reflecting SDEs with distribution dependent noise are also studied.

Probability