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

Summary 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.