Kinetic McKean-Vlasov SDEs with Hölder coefficients and law-dependent diffusion are weakly well-posed under a weak Hörmander condition.
Optimal regularity for degenerate Kolmogorov equations in non-divergence form with rough-in-time coefficients
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Well-posedness of kinetic McKean-Vlasov equations
Kinetic McKean-Vlasov SDEs with Hölder coefficients and law-dependent diffusion are weakly well-posed under a weak Hörmander condition.