Dynamics of Optimal Partial Transport

Original · EN

This paper considers the evolution dynamics of the free boundaries in terms of the change of m, the allowed amount of transported mass or the change of λ, the transportation cost cap, i.e. the allowed maximum cost for a unit mass to be transported. Focusing on the quadratic cost function, we show Hölder and Lipschitz estimates on the speed of the free boundary motion in terms of m and λ, respectively. It is also shown that the parameter m is a Lipschitz function of λ, which previously was known only to be a continuous increasing function Ca-Mc.