Spherical Hellinger-Kantorovich gradient flows

2018/09/10 by Stanislav Kondratyev, Dmitry Vorotnikov, Kondratyev, Stanislav +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.1809.03430

arxiv created 2019/04/02 · arxiv updated 2019/04/03

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.

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