| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 42 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2018042 | |
| Published online | 20 September 2019 | |
On the total variation Wasserstein gradient flow and the TV-JKO scheme
1
Ceremade, UMR CNRS 7534, Université Paris Dauphine, Pl. de Lattre de Tassigny,
75775
Paris Cedex 16, France.
2
MOKAPLAN,
INRIA-Paris, France.
3
Centre for Mathematical Sciences, University of Cambridge,
Wilberforce Rd,
Cambridge
CB3 0WA, UK.
* Corresponding author: carlier@ceremade.dauphine.fr
Received:
20
March
2018
Accepted:
11
July
2018
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.
Mathematics Subject Classification: 35G31 / 49N15
Key words: Total variation / Wasserstein gradient flows / JKO scheme / fourth-order evolution equations
© EDP Sciences, SMAI 2019
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