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J. Carrillo, A. Jüngel, M. Santos:
"Displacement convexity for the entropy in semidiscrete nonlinear Fokker-Planck equations";
in: "ASC Report 26/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 18.

The displacement λ-convexity of a nonstandard entropy with respect to a nonlocal transportation metric in finite state spaces is shown using a gradient flow ap-proach. The constant λ is computed explicitly in terms of a priori estimates of the solution to a finite-difference approximation of a nonlinear Fokker-Planck equation. The key idea is to employ a new mean function, which defines the Onsager operator in the gradient flow formulation.

Entropy, displacement convexity, logarithmic mean, finite differences, fast-diffusion equation

http://www.asc.tuwien.ac.at/preprint/2016/asc26x2016.pdf