16 citations · 34 across the 20 of their papers we have counts for
23 papers
Kantorovich type topologies on spaces of measures and convergence of barycenters
Konstantin A. Afonin, Vladimir I. Bogachev
We study two topologies and on the space of measures on a completely regular space generated by Kantorovich--Rubinshtein and Kantorovich seminorms analogous to their…
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…
Optimal transportation of measures with a parameter
Vladimir Bogachev, Svetlana Popova
We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in…
Markov uniqueness and Fokker-Planck-Kolmogorov equations
Sergio Albeverion, Vladimir I. Bogachev, Michael Röckner
In this paper we show that Markov uniqueness for symmetric pre-Dirichlet operators follows from the uniqueness of the corresponding Fokker-Planck-Kolmogorov equation (FPKE). Si…
Regularity of solutions to Kolmogorov equations with perturbed drifts
Vladimir I. Bogachev, Egor D. Kosov, Alexander V. Shaposhnikov
We prove that a probability solution of the stationary Kolmogorov equation generated by a first order perturbation of the Ornstein--Uhlenbeck operator possesses a highly in…
Kantorovich problems and conditional measures depending on a parameter
Vladimir Bogachev, Il'ya Malofeev
We study measurable dependence of measures on a parameter in the following two classical problems: constructing conditional measures and the Kantorovich optimal transportation. We…