论文标题
相对于各向异性的各向异性花栗鼠常数的优化
Optimization of the anisotropic Cheeger constant with respect to the anisotropy
论文作者
论文摘要
给定一个开放的，有界的集合$ω$中的$ \ mathbb {r}^n $，我们考虑在相关的单位球的体积约束下，相对于各向异性$ k $，各向异性cheeger常数$ h_k（ω）$相对于各向异性$ k $。在平面案例中，假设$ k $是一个凸，中央对称的机构，我们证明了最小化器的存在。此外，如果$ω$是一个球，我们表明最佳各向异性$ k $不是球，并且在所有常规多边形中，广场可提供最小的价值。
Given an open, bounded set $Ω$ in $\mathbb{R}^N$, we consider the minimization of the anisotropic Cheeger constant $h_K(Ω)$ with respect to the anisotropy $K$, under a volume constraint on the associated unit ball. In the planar case, under the assumption that $K$ is a convex, centrally symmetric body, we prove the existence of a minimizer. Moreover, if $Ω$ is a ball, we show that the optimal anisotropy $K$ is not a ball and that, among all regular polygons, the square provides the minimal value.
