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

Carlier, Guillaume; Poon, Clarice (2019), On the total variation Wasserstein gradient flow and the TV-JKO scheme, ESAIM. Control, Optimisation and Calculus of Variations, 25, p. 21. 10.1051/cocv/2018042

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
ESAIM. Control, Optimisation and Calculus of Variations
Volume
25
Publisher
EDP Sciences
Pages
21
Publication identifier
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Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Poon, Clarice
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Applied Mathematics and Theoretical Physics [DAMTP]
Abstract (EN)
We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a sort of maximum principle and the regularity of level sets). We study in detail the case of step functions. Finally, in dimension one, we establish convergence as the time step goes to zero to a solution of a fourth-order nonlinear evolution equation.
Subjects / Keywords
fourth-order evolution equations; JKO scheme; total variation; Wasserstein gradient flows