Local and Global Minimality Results for a Nonlocal Isoperimetric Problem on ℝN
Local and Global Minimality Results for a Nonlocal Isoperimetric Problem on ℝN
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ℝN 上非局部等周问题的局部和全局极小值结果
DOI：
10.1137/130929898
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
R. Cristoferi
中科院分区：
文献类型：
--
作者：
M. Bonacini;R. Cristoferi
考虑一个定义在全空间$\mathbb{R}^N$中的非局部等周问题，其非局部部分由指数为$\alpha\in（0，N-1）$的Riesz势给出.我们证明了具有正二次变差的临界组态是局部极小元，并且满足关于L^1 $-范数的一个数量不等式。这个标准提供了一个（明确确定的）临界阈值的存在，确定球是一个局部极小的体积的间隔，它使我们能够解决几个全球极小问题。
We consider a nonlocal isoperimetric problem defined in the whole space $\mathbb{R}^N$, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0,N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the $L^1$-norm. This criterion provides the existence of an (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and it allows us to address several global minimality issues.