On the total variation Wasserstein gradient flow and the TV-JKO scheme Article Swipe
Related Concepts
Variation (astronomy)
Scheme (mathematics)
Balanced flow
Flow (mathematics)
Mathematics
Mathematical analysis
Physics
Geometry
Astrophysics
Guillaume Carlier
,
Clarice Poon
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1051/cocv/2018042
· OA: W2593850721
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1051/cocv/2018042
· OA: W2593850721
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.
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