On the Jordan�Kinderlehrer�Otto variational scheme and constrained optimization in the Wasserstein metric

Tudorascu, Adrian
June 2008
Calculus of Variations & Partial Differential Equations;Jun2008, Vol. 32 Issue 2, p155
Academic Journal
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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