Smoothness of the density for McKean-Vlasov SDEs with measurable kernel

Yi Han

Consider the McKean-Vlasov SDE $$d{X}_t=⟨b(X_t-\cdot ),{\mu }_t⟩dt+d{W}_t,{\mu }_t=\mathrm{Law}(X_t),$$ where $W$ is the $n$-dimensional Brownian motion and $b:\mathbb…