Author： Tudorascu Adrian
Publisher： Springer Publishing Company
ISSN： 0944-2669
Source： Calculus of Variations and Partial Differential Equations, Vol.32, Iss.2, 2008-06, pp. : 155-173
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Abstract
We prove the monotonicity of the second-order moments of the discrete approximations to the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This issue appears in the study of constrained optimization in the 2-Wasserstein metric performed by Carlen and Gangbo for the kinetic Fokker–Planck equation. As an alternative to their duality method, we provide the details of a direct approach, via Lagrange multipliers. Estimates for the fourth-order moments in the constrained case, which are essential to the subsequent alternate analysis, are also obtained.
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