preprint
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Inserted: 11 nov 2026
Last Updated: 11 nov 2026

Year: 2026

Abstract:

We study the approximation of functionals by geodesically semiconvex functionals in the Wasserstein space, with applications to dissipation estimates along the Jordan-Kinderlehrer-Otto (JKO) scheme. For the potential and interaction energies, the approximation problem reduces to approximate the underlying potentials in Euclidean space. For the internal energies, we construct approximations by decomposing truncated functionals into differences of geodesically convex functionals and applying Moreau-Yosida regularization to the second component. Under suitable assumptions, we establish strong quantitative convergence of the gradient of the first variation in weighted \(L^2\) space. These approximations may enable us to obtain dissipation estimates along the JKO scheme for functionals that are not geodesically semiconvex. We illustrate this approach by deriving an \(L^{m+1}\) bound for the JKO scheme of fast diffusion equation, and by establishing internal energy dissipation for the JKO scheme of Fokker-Planck equation.

Tags: EYAWKAJKOS