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Spherical Hellinger-Kantorovich gradient flows
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Type: Preprint
National /International: International
Title: Spherical Hellinger-Kantorovich gradient flows
Publication Date: 2018-09-11
Authors: - Stanislav Kondratyev
- Dmitry Vorotnikov
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.
Institution: DMUC 18-31
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