AI 中文总结
研究有界凸域间二次最优传输凸势函数的全局 $W^{2,p}$ 估计，在源和目标密度连续且有界条件下，不设域边界正则性条件得出相关估计。
AI 中文摘要
本文针对有界凸域之间二次最优传输的凸势函数建立了全局 $W^{2,p}$ 估计。假设源密度和目标密度仅连续且远离零和无穷大，并且不对域边界施加正则性条件。
英文摘要
In this paper we establish global $W^{2,p}$ estimates for the convex potentials of quadratic optimal transport between bounded convex domains with continuous positive densities. All the assumptions are optimal. The main new ideas include a blow-up analysis that allows for lower-dimensional collapse of the limiting source measure and reduces the limiting problem to a transport problem on its affine hull, and a good-bad scale decomposition in which rigidity controls the good scales while a counting argument shows that the proportion of bad scales tends to zero.
