论文标题
用多面体和Y形奇异性的Monge-ampère方程解决方案
Solutions to the Monge-Ampère equation with polyhedral and Y-shaped singularities
论文作者
论文摘要
我们在$ \ mathbb {r}^3 $和$ \ mathbb {r}^4 $上构建凸功能，这是对Monge-ampère方程的平滑解决方案$ \ det d^2u = 1 $ = 1 $远离紧凑的一维单数集，可以是y型或形成侧侧的Edges的侧面。这些示例在Alexandrov Sense中求解了方程式，从有限的许多点远离。我们的方法基于解决障碍物的障碍物问题，其中障碍物的图是凸多物件。
We construct convex functions on $\mathbb{R}^3$ and $\mathbb{R}^4$ that are smooth solutions to the Monge-Ampère equation $\det D^2u = 1$ away from compact one-dimensional singular sets, which can be Y-shaped or form the edges of a convex polytope. The examples solve the equation in the Alexandrov sense away from finitely many points. Our approach is based on solving an obstacle problem where the graph of the obstacle is a convex polytope.
