Mini-course of lectures on modern analysis: "Stationary Kolmogorov equations". Lecture 2.

Interest in the stationary Kolmogorov or Fokker-Planck–Kolmogorov equations is associated with the construction and study of invariant measures of diffusion processes. In addition, the Kolmogorov equation is the most important example of a doubly divergent elliptic equation. The properties of solutions of doubly divergent elliptic equations differ significantly from the properties of classical elliptic partial differential equations, for example, there is no improvement in the smoothness of solutions compared to the smoothness of coefficients. The course will present recent results on the existence, uniqueness and regularity of solutions. In addition, we will discuss estimates of distances between solutions and their application to nonlinear stationary Kolmogorov equations.