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arXiv · 2610.01928

Global regularity and sparsity for regularised optimal transport

Xiaopeng Cheng·Lukas Koch·Haotian Xiao
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Abstract

We study regularised optimal transport with subquadratic or entropic regularisation. Under $C^{1,α}$-assumptions on the marginals and the domains of their support, we prove global gradient-Lipschitz bounds on the potentials, uniform in the regularisation parameter. Moreover, we show that, up to the boundary, the support of the conditional supports $\text{supp}\,π_\varepsilon(\cdot|x)$ behaves like balls of radius $\varepsilon^\frac 4 {d(p-1)+2}$. Our work was carried out concurrently and independently of [9]. We obtain the results of [9,Theorem 1.2] under weaker assumptions and with a different proof.

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Xiaopeng Cheng, Lukas Koch, Haotian Xiao. 2026-10-01. Global regularity and sparsity for regularised optimal transport. https://arxiv.org/abs/2610.01928

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