On the Cheeger sets in strips and non-convex domains
On the Cheeger sets in strips and non-convex domains
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关于条带和非凸域中的 Cheeger 集
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Pratelli
中科院分区：
文献类型：
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作者：
G. P. Leonardi;A. Pratelli
在本文中，我们考虑了非convex域的Cheeger问题，对平面条具有特别的兴趣，近年来我们的主要结果是对串带的估计，这是一个强大的cheeger strips。比以前从Krejči树和Pratelli所知道的（Pac J Math 254（2）：309–333，2011），并证明条带与凸形域共享许多关键属性此外，我们尊重Cheeger问题。
In this paper we consider the Cheeger problem for non-convex domains, with a particular interest in the case of planar strips, which have been extensively studied in recent years. Our main results are an estimate on the Cheeger constant of strips, which is stronger than the previous one known from Krejčiřík and Pratelli (Pac J Math 254(2):309–333, 2011), and the proof that strips share with convex domains a number of crucial properties with respect to the Cheeger problem. Moreover, we present several counterexamples showing that the same properties are not valid for generic non-convex domains.