A new $L^\infty$ estimate in optimal mass transport
A new $L^\infty$ estimate in optimal mass transport
Let $\Omega$ be a bounded Lipschitz regular open subset of $\mathbb {R}^d$ and let $\mu ,\nu$ be two probablity measures on $\overline {\Omega }$. It is well known that if $\mu =f dx$ is absolutely continuous, then there exists, for every $p>1$, a unique transport map $T_p$ pushing forward $\mu$ …