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

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 approach. 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.

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