BV estimates in optimal transportation and their applications

par Alpar Meszaros (Université Paris Sud)

vendredi 7 nov. 2014, 10:00 → 10:45 Europe/Paris

XLIM Salle X.203

We present some total variation estimates for the minimizers of some functionals involving the 2-Wasserstein distance. As applications we study the regularity properties of projected measures in the Wasserstein sense, and with the help of this we build splitting type algorithms to treat diffusive crowd motion models with congestion effect. As a byproduct we prove the (well-known) total variation decay estimate for the solutions of the porous medium equation via optimal transportation techniques. If time permits, we make as well some links with the optimal partial transport problem. The talk is based on some joint works with G. De Philippis, F. Santambrogio and B. Velichkov.