44 citations · 51 across the 6 of their papers we have counts for
9 papers
Convex Sobolev inequalities related to unbalanced optimal transport
Stanislav Kondratyev, Dmitry Vorotnikov
We study the behaviour of various Lyapunov functionals (relative entropies) along the solutions of a family of nonlinear drift-diffusion-reaction equations coming from statistical…
Spherical Hellinger-Kantorovich gradient flows
Stanislav Kondratyev, Dmitry Vorotnikov
We study nonlinear degenerate parabolic equations of Fokker-Planck type which can be viewed as gradient flows with respect to the recently introduced spherical Hellinger-Kantorovic…
Nonlinear Fokker-Planck equations with reaction as gradient flows of the free energy
Stanislav Kondratyev, Dmitry Vorotnikov
We interpret a class of nonlinear Fokker-Planck equations with reaction as gradient flows over the space of Radon measures equipped with the recently introduced Hellinger-Kantorovi…
Bounds on the number of vertices of sublattice-free lattice polygons
Nikolai Bliznyakov, Stanislav Kondratyev
In this paper we establish bounds on the number of vertices for a few classes of convex sublattice-free lattice polygons. The bounds are essential for proving the formula for the c…
Existence of sublattice points in lattice polygons
Nikolai Bliznyakov, Stanislav Kondratyev
We state the formula for the critical number of vertices of a convex lattice polygon that guarantees that the polygon contains at least one point of a given sublattice and give a p…
A new multicomponent Poincaré-Beckner inequality
S. Kondratyev, L. Monsaingeon, D. Vorotnikov
We prove a new vectorial functional inequality of Poincaré-Beckner type. The inequality may be interpreted as an entropy-entropy production one for a gradient flow in the metric sp…
A fitness-driven cross-diffusion system from polulation dynamics as a gradient flow
Stanislav Kondratyev, Léonard Monsaingeon, Dmitry Vorotnikov
We consider a fitness-driven model of dispersal of interacting populations, which was previously studied merely in the case . Based on some optimal transport distance rece…
A new optimal transport distance on the space of finite Radon measures
Stanislav Kondratyev, Léonard Monsaingeon, Dmitry Vorotnikov
We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equ…
On the bulk velocity of Brownian ratchets
Stanislav Kondratyev, José Miguel Urbano, Dmitry Vorotnikov
In this paper we study the unidirectional transport effect for Brownian ratchets modeled by Fokker-Planck-type equations. In particular, we consider the adiabatic and semiadiabatic…