发表机构
Max Planck Institute for Mathematics in the Sciences; University of Sussex（马克斯·普朗克科学促进部数理研究所; 萨塞克斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究次二次或熵正则化最优输运，在边缘分布满足$C^{1,\alpha}$假设下，证明势函数全局梯度-Lipschitz界关于正则化参数一致，并刻画条件支撑集为半径$\varepsilon^{4/(d(p-1)+2)}$的球，在更弱假设下独立获得文献[9]的结果。
AI 中文摘要
我们研究具有次二次或熵正则化的正则化最优输运问题。在边缘分布及其支撑域满足$C^{1,\alpha}$假设的条件下，我们证明了势函数的全局梯度-Lipschitz界，且该界关于正则化参数一致。此外，我们证明了，直至边界，条件支撑集$\text{supp}\\,\pi_\varepsilon(\cdot|x)$的支撑表现为半径为$\varepsilon^\frac 4 {d(p-1)+2}$的球。我们的工作与文献[9]同时且独立进行。我们在更弱的假设下，以不同的证明方法获得了文献[9]定理1.2的结果。
英文摘要
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.
Commentsv2. Some small typos in text and bibliography corrected
