论文标题
将全球解决方案完全分类用于障碍问题
Complete classification of global solutions to the obstacle problem
论文作者
论文摘要
在$ \ Mathbb {r}^n $中或等效于零正流域等于$ \ Mathbb {r}^n $中的全球解决方案的表征已在90多年来进行了研究。在本文中，我们通过证明以下长期的猜想来对这个问题做出确定的答案：全球解决障碍问题的巧合集是半空间，椭圆形，抛物线或具有椭球或抛物线的圆柱体。
The characterization of global solutions to the obstacle problems in $\mathbb{R}^N$, or equivalently of null quadrature domains, has been studied over more than 90 years. In this paper we give a conclusive answer to this problem by proving the following long-standing conjecture: The coincidence set of a global solution to the obstacle problem is either a half-space, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base.
