  The main result of this paper is the existence of an optimal transport map
$T$ between two given measures $\mu$ and $\nu$, for a cost which considers the
maximal oscillation of $T$ at scale $\delta$, given by
$\omega_\delta(T):=\sup_{|x-y|<\delta}|T(x)-T(y)|$. The minimization of this
criterion finds applications in the field of privacy-respectful data
transmission. The existence proof unfortunately only works in dimension one and
is based on some monotonicity considerations.
