On the total variation Wasserstein gradient flow and the TV-JKO scheme

Guillaume Carlier, Clarice Poon

Research output: Contribution to journalArticle


We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a form of maximum principle and in some cases, a minimum principle as well). Finally, we establish a convergence result as the time step goes to zero to a solution of a fourth-order nonlinear evolution equation, under the additional assumption that the density remains bounded away from zero, this lower bound is shown in dimension one and in the radially symmetric case.
Original languageEnglish
Article number42
Number of pages21
JournalEsaim-Control Optimisation and Calculus of Variations
Early online date20 Sep 2019
Publication statusPublished - 2019

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