4 papers
Infinite-dimensional nonlinear stationary Fokker-Planck-Kolmogorov equations
Vladimir I. Bogachev, Michael Röckner, Stanislav V. Shaposhnikov
We prove existence of a probability solution to the nonlinear stationary Fokker-Planck-Kolmogorov equation on an infinite dimensional space with a centered Gaussian measure wi…
The Dirichlet problem for double divergence form elliptic equations with measures as boundary conditions
V. I. Bogachev, S. V. Shaposhnikov
We introduce and study the Dirichlet problem for double divergence form elliptic equations with coefficients of low regularity and boundary conditions given by general Borel measur…
Estimates for the distances between solutions to Kolmogorov equations with diffusion matrices of low regularity
Vladimir I. Bogachev, Stanislav V. Shaposhnikov
We obtain estimates for the weighted -norm of the difference of two probability solutions to Kolmogorov equations in terms of the difference of the diffusion matrices and the…
Doubling variables and uniqueness of probability solutions to degenerate stationary Kolmogorov equations
V. I. Bogachev, S. V. Shaposhnikov, D. V. Shatilovich
We obtain sufficient conditions for the uniqueness of a probability solution to the stationary Kolmogorov equation with a degenerate diffusion matrix. We employ the method of doubl…