Spherical Hellinger-Kantorovich gradient flows
Functional Analysis
2019-04-03 v2 Analysis of PDEs
Abstract
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-Kantorovich distance. The driving entropy is not assumed to be geodesically convex. We prove solvability of the problem and the entropy-entropy production inequality, which implies exponential convergence to the equilibrium. As a corollary, we obtain some related results for the Wasserstein gradient flows. We also deduce transportation inequalities in the spirit of Talagrand, Otto and Villani for the spherical and conic Hellinger-Kantorovich distances.
Cite
@article{arxiv.1809.03430,
title = {Spherical Hellinger-Kantorovich gradient flows},
author = {Stanislav Kondratyev and Dmitry Vorotnikov},
journal= {arXiv preprint arXiv:1809.03430},
year = {2019}
}