Uniqueness for a class of stochastic Fokker-Planck and porous media equations

Röckner M, Russo F. Uniqueness for a class of stochastic Fokker-Planck and porous media equations. Journal of Evolution Equations. 2017;17(3):1049-1062.The purpose of the present note consists of first showing a uniqueness result for a stochastic Fokker-Planck equation under very general assumptions. In particular, the second-order coefficients may be just measurable and degenerate. We also provide a proof for uniqueness of a stochastic porous media equation in a fairly large space