On the total variation Wasserstein gradient flow and the TV-JKO scheme
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 42.

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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018042
Classification : 35G31, 49N15
Mots-clés : Total variation, Wasserstein gradient flows, JKO scheme, fourth-order evolution equations
Carlier, Guillaume 1 ; Poon, Clarice 1

1 
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Carlier, Guillaume; Poon, Clarice. On the total variation Wasserstein gradient flow and the TV-JKO scheme. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 42. doi : 10.1051/cocv/2018042. http://www.numdam.org/articles/10.1051/cocv/2018042/

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