<Reference List> | |
Type: | Preprint |
National /International: | International |
Title: | Convex Sobolev inequalities related to unbalanced optimal transport |
Publication Date: | 2019-04-08 |
Authors: |
- Stanislav Kondratyev
- Dmitry Vorotnikov |
Abstract: | 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 equippedcwith 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. |
Institution: | DMUC 19-13 |
Online version: | http://www.mat.uc.pt...prints/eng_2019.html |
Download: | Not available |