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arXiv · 2106.02899

$L^\infty$-estimates in optimal transport for non quadratic costs

Cristian E. Gutiérrez·Annamaria Montanari
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Abstract

For cost functions $c(x,y)=h(x-y)$ with $h\in C^2$ homogeneous of degree $p\geq 2$, we show $L^\infty$-estimates of $Tx-x$ on balls, where $T$ is an $h$-monotone map. Estimates for the interpolating mappings $T_t=t(T-I)+I$ are deduced from this.

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Cristian E. Gutiérrez, Annamaria Montanari. 2021-06-05. $L^\infty$-estimates in optimal transport for non quadratic costs. https://arxiv.org/abs/2106.02899

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