Uniqueness of degenerate Fokker-Planck equations with weakly differentiable drift whose gradient is given by a singular integral

Abstract

In this paper we prove the uniqueness of solutions to degenerate Fokker-Planck equations with bounded coefficients, under the additional assumptions that the diffusion coefficient has $W^{1,2}_{loc}$ regularity, while the gradient of the drift coefficient is merely given by a singular integral.