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

par Kexin Lin

mercredi 29 mai 2024, 10:30 → 12:00 Europe/Paris

In this talk, I will present a paper by Guillaume Carlier and Clarice Poon concerning the gradient flow of the total variation in Wasserstein metric and its related PDE. We will first study the discrete TV-JKO scheme, characterizing the optimizers and a form of maximum principle. Then we will prove the convergence of JKO steps as τ → 0+ to a fourth-order nonlinear evolution equation under the extra assumption that densities remain bounded aways from zero(a form of minimum principle).