AI 中文总结
本文研究Monge-Ampère障碍问题自由边界直到边界的正则性，发现边界值增长阶影响正则性，且二次增长下高维正则性优于二维。
AI 中文摘要
本文研究Monge-Ampère障碍问题中自由边界直到边界的正则性。我们主要关注接触点附近边界值的增长阶对正则性的影响。我们还发现一个有趣的现象：在二次增长的边界值下，自由边界在高维空间中比在二维空间中具有更好的正则性。
英文摘要
In this paper, we study the regularity of free boundaries for Monge-Ampère obstacle problem up to the boundary. We mainly focus on how the growth order of boundary value near the contact point impact the regularity. We also find an interesting phenomena that under quadratic growth boundary value, the free boundary enjoys better regularity in high dimensions than in two dimension.
Comments22 pages, 3 figures
