4 citations · 18 across the 12 of their papers we have counts for
13 papers
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…
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 wit…
Zvonkin's transform and the regularity of solutions to double divergence form elliptic equations
Vladimir I. Bogachev, Michael Röckner, Stanislav V. Shaposhnikov
We study qualitative properties of solutions to double divergence form elliptic equations (or stationary Kolmogorov equations) on~. It is shown that the Harnack inequ…
On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations
Vladimir I. Bogachev, Michael Röckner, Stanislav V. Shaposhnikov
We prove a generalization of the known result of Trevisan on the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to the Cauchy problem for the Fokker-Pl…
Log-Sobolev-type inequalities for solutions to stationary Fokker-Planck-Kolmogorov equations
V. I. Bogachev, A. V. Shaposhnikov, S. V. Shaposhnikov
We prove that every probability measure satisfying the stationary Fokker-Planck-Kolmogorov equation obtained by a -integrable perturbation of the drift term of the…