$L^\infty$-optimal transport for a class of quasiconvex cost functions

Camilla Brizzi; Luigi De Pascale; Anna Kausamo

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arXiv · 2104.08074

$L^\infty$-optimal transport for a class of quasiconvex cost functions

Camilla Brizzi·Luigi De Pascale·Anna Kausamo

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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.

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Camilla Brizzi, Luigi De Pascale, Anna Kausamo. 2021-04-16. $L^\infty$-optimal transport for a class of quasiconvex cost functions. https://arxiv.org/abs/2104.08074

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