标题： 多边形上带有Guillemin边界条件的Monge-Ampère方程的边界估计 显示英文标题

标题： Boundary Estimates for the Monge-Ampère Equation in the Polygons with Guillemin Boundary Conditions

摘要： 我们建立了一个二维奇异蒙日-安培方程在凸多面体上具有吉勒明边界条件的施瓦茨型边界正则性结果。 这扩展了鲁宾和黄之前的成果，适用于右边更不规则的情况；具体来说，是赫尔德连续函数。 我们的方法严重依赖唐纳森在他关于阿布雷方程的一系列论文中开发的复杂技术。 显示英文摘要

摘要： We establish a Schauder-type boundary regularity result for a two-dimensional singular Monge-Amp\'ere equation on convex polytopes with Guillemin boundary conditions. This extends the previous work of Rubin and Huang to the case where the right-hand side is less regular; specifically, H\"older continuous functions. Our method relies heavily on the sophisticated techniques developed by Donaldson in his series of papers on the Abreu equation.