The fractional Cheeger problem
The fractional Cheeger problem
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DOI：
10.4171/ifb/325
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
L. Brasco;E. Lindgren;E. Parini
中科院分区：
文献类型：
--
作者：
L. Brasco;E. Lindgren;E. Parini
给定一个开有界集$\Omega\subset\mathbb{R}^N$，考虑极小化$\Omega$的子集之间的$s-$周长与$N-$维Lebesgue测度之比的问题.这是著名的Cheeger问题的非局部版本。我们证明了这个问题的最优集的各种性质，以及一些等价的配方。此外，一些非线性和非局部特征值问题的极限行为进行了研究，在此优化问题。演示文稿尽可能独立。
Given an open and bounded set $\Omega\subset\mathbb{R}^N$, we consider the problem of minimizing the ratio between the $s-$perimeter and the $N-$dimensional Lebesgue measure among subsets of $\Omega$. This is the nonlocal version of the well-known Cheeger problem. We prove various properties of optimal sets for this problem, as well as some equivalent formulations. In addition, the limiting behaviour of some nonlinear and nonlocal eigenvalue problems is investigated, in relation with this optimization problem. The presentation is as self-contained as possible.