Published Paper

Inserted: 7 mar 2024
Last Updated: 7 mar 2024

Journal: J. Math. Anal. Appl.
Volume: 527
Number: 1
Pages: Paper No. 127331, 18
Year: 2023
Doi: 10.1016/j.jmaa.2023.127331

Abstract:

We consider the $L^\infty$-optimal mass transportation problem \[ \min_{\Pi(\mu, \nu)} \gamma-\mathrm{ess\,sup\,} c(x,y), \] for a new class of costs $c(x,y)$ for which we introduce a tentative notion of twist condition. In particular we study the conditions under which the infinitely-motonone minimizers are induced by a transportation map. We also state a uniqueness result for infinitely cyclically monotone Monge minimizers that corresponds to this class of cost functions. We compare the results to previous works.