Convex Sobolev inequalities related to unbalanced optimal transport

Autor:	Kondratyev, Stanislav, Vorotnikov, Dmitry
Rok vydání:	2019
Předmět:	Mathematics - Functional Analysis Mathematics - Analysis of PDEs 26D10 35K57 35B40 49Q20 58B20
Druh dokumentu:	Working Paper
Popis:	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 mechanics and population dynamics. These equations can be viewed as gradient flows over the space of Radon measures equipped with the Hellinger-Kantorovich distance. The driving functionals of the gradient flows are not assumed to be geodesically convex or semi-convex. We prove new isoperimetric-type functional inequalities, allowing us to control the relative entropies by their productions, which yields the exponential decay of the relative entropies.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.04112 Zobrazit plný text záznamu View this record from Arxiv