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arXiv · 1703.00243

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

Guillaume Carlier·Clarice Poon
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Abstract

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.

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Guillaume Carlier, Clarice Poon. 2017-03-01. On the total variation Wasserstein gradient flow and the TV-JKO scheme. https://arxiv.org/abs/1703.00243

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