Rigidity results for variational infinity ground states
Rigidity results for variational infinity ground states
复制标题
变分无穷大基态的刚性结果
DOI：
10.1512/iumj.2019.68.7617
复制
发表时间：
2017
影响因子：
1.1
通讯作者：
I. Fragalà
中科院分区：
文献类型：
--
作者：
G. Crasta;I. Fragalà
我们证明了开有界凸域$\Omega \subset \mathbb{R}^n$的变分无穷基态$u$的两个刚性结果。他们指出，$u$与距离$\Omega$的边界的距离的倍数一致，如果$|纳卜拉乌|$在$\partial \Omega$上是常数，或者$u$在$\Omega$的高岭之外属于$C ^ {1，1}$类。因此，在这两种情况下，$\Omega$可以在几何上被描述为“体育场状域”。
We prove two rigidity results for a variational infinity ground state $u$ of an open bounded convex domain $\Omega \subset \mathbb{R}^n$. They state that $u$ coincides with a multiple of the distance from the boundary of $\Omega$ if either $|\nabla u|$ is constant on $\partial \Omega$, or $u$ is of class $C ^ {1,1}$ outside the high ridge of $\Omega$. Consequently, in both cases $\Omega$ can be geometrically characterized as a "stadium-like domain".