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.
|Number of pages||21|
|Journal||Esaim-Control Optimisation and Calculus of Variations|
|Early online date||20 Sept 2019|
|Publication status||Published - 2019|