A survey of the regularity properties of solutions to Fokker-Planck-Kolmogorov equations of elliptic and parabolic types is presented. We discuss conditions for the existence of solution densities, the local properties of these densities like boundedness, continuity, Hölder continuity, Sobolev differentiability, and also the global properties such as bounds on the whole space, high integrability, and membership in Sobolev classes on the whole space. Some new results on the properties of solutions in the case of coefficients of low regularity are presented. Bibliography: 101 titles.
Bogachev et al. (Wed,) studied this question.