Convex Sobolev inequalities related to unbalanced optimal transport
Functional Analysis
2019-04-09 v1 Analysis of PDEs
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 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.
Keywords
Cite
@article{arxiv.1904.04112,
title = {Convex Sobolev inequalities related to unbalanced optimal transport},
author = {Stanislav Kondratyev and Dmitry Vorotnikov},
journal= {arXiv preprint arXiv:1904.04112},
year = {2019}
}