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arXiv · 1611.04716

Displacement convexity for the entropy in semidiscrete nonlinear Fokker-Planck equations

José A. Carrillo·Ansgar Jüngel·Matheus C. Santos
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Abstract

The displacement $\lambda$-convexity of a nonstandard entropy with respect to a nonlocal transportation metric in finite state spaces is shown using a gradient flow approach. The constant $\lambda$ 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.

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José A. Carrillo, Ansgar Jüngel, Matheus C. Santos. 2016-11-15. Displacement convexity for the entropy in semidiscrete nonlinear Fokker-Planck equations. https://arxiv.org/abs/1611.04716

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