BV estimates in optimal transportation and their applications
par
Alpar Meszaros(Université Paris Sud)
→
Europe/Paris
XLIM Salle X.203
XLIM Salle X.203
FST-Université de Limoges,
123, Av. Albert Thomas.
Description
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.