Before revision: In this paper, we first establish well-posedness results of McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a  drift coefficient that is discontinuous in the spatial component . The analysis is restricted to the one-dimensional case, and we only require a fairly mild condition on the diffusion coefficient, namely to be non-zero in a point of discontinuity  , while we need to impose certain structural assumptions on the measure-dependence of the drift.
After revision: In this paper, we first establish well-posedness results of McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a drift coefficient that is discontinuous in the spatial component , and a diffusion coefficient which is a Lipschitz function of the state only. We only require a fairly mild condition on the diffusion coefficient, namely to be non-zero in a point of discontinuity , while we need to impose certain structural assumptions on the measure-dependence of the drift.