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

Carlier, Guillaume; Poon, Clarice (2017-03), On the total variation Wasserstein gradient flow and the TV-JKO scheme. https://basepub.dauphine.fr/handle/123456789/16904

Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01492343
Date
2017-03
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
28
Metadata
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Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Poon, Clarice
Department of Applied Mathematics and Theoretical Physics [DAMTP]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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