论文标题
过度确定的问题和无界域中的相对Cheeger设置
Overdetermined problems and relative Cheeger sets in unbounded domains
论文作者
论文摘要
在本文中，我们研究了无限制集合$ \ Mathcal c $中包含的域$ω$的部分过度确定的混合边界值问题。我们介绍了相对于$ \ Mathcal C $的Cheeger集的概念，并表明，如果域$ω\ subset \ Mathcal c $允许解决过度确定的问题的解决方案，那么它与其相对的脸颊集合。我们还研究了$ \ Mathcal c $内部表征恒定平均曲率表面$γ$的相关问题。在$ \ Mathcal c $的情况下，每当$ω$的相对边界或表面$γ$的相对边界是气缸底部的图形时，我们就会获得进一步的结果。
In this paper we study a partially overdetermined mixed boundary value problem for domains $Ω$ contained in an unbounded set $\mathcal C$. We introduce the notion of Cheeger set relative to $\mathcal C$ and show that if a domain $Ω\subset \mathcal C$ admits a solution of the overdetermined problem, then it coincides with its relative Cheeger set. We also study the related problem of characterizing constant mean curvature surfaces $Γ$ inside $\mathcal C$. In the case when $\mathcal C$ is a cylinder we obtain further results whenever the relative boundary of $Ω$ or the surface $Γ$ is a graph on the base of the cylinder.
