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

被引：4

作者：

Carlier, Guillaume ^{[1
,2
]}

Poon, Clarice ^{[3
]}

机构：

[1] Univ Paris 09, Ceremade, UMR 7534, CNRS, Pl Lattre de Tassigny, F-75775 Paris 16, France

[2] INRIA Paris, MOKAPLAN, Paris, France

[3] Univ Cambridge, Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WA, England

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2019年 / 25卷

关键词：

Total variation; Wasserstein gradient flows; JKO scheme; fourth-order evolution equations; EQUATIONS; EXISTENCE; SETS;

D O I：

10.1051/cocv/2018042

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页数：21

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