Optimal boundary regularity for a singular Monge-Ampere equation
Optimal boundary regularity for a singular Monge-Ampere equation
复制标题
奇异 Monge-Ampere 方程的最优边界正则性
DOI：
10.1016/j.jde.2018.01.051
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发表时间：
2018
影响因子：
2.4
通讯作者：
Li You
中科院分区：
文献类型：
--
作者：
Jian Huaiyu;Li You
本文研究了几个几何问题产生的奇异Monge-Ampère型方程的最优全局正则性。我们发现，全局正则性不依赖于区域的光滑性，而依赖于区域的凸性。我们引入(a，η)型来描述凸性。结果表明，区域越凸，解的正则性越好。尤其是在角点附近的正则性最好。
In this paper we study the optimal global regularity for a singular Monge–Ampère type equation which arises from a few geometric problems. We find that the global regularity does not depend on the smoothness of domain, but it does depend on the convexity of the domain. We introduce (a, η) type to describe the convexity. As a result, we show that the more convex is the domain, the better is the regularity of the solution. In particular, the regularity is the best near angular points.