From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials
From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials
复制标题
从径向对称到排斥-吸引势聚集平衡的分形行为
DOI：
10.1007/s00526-022-02368-4
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发表时间：
2022
影响因子：
2.1
通讯作者：
Carrillo J
中科院分区：
文献类型：
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作者：
Carrillo J
对于具有排斥-吸引势能的相互作用能，我们给出了保证无限 Wasserstein 距离中局部极小值的径向对称性的一般条件。因此，我们获得了该拓扑中一类相互作用势的局部极小值的唯一性。我们引入了相互作用势凹性的新概念，使我们能够展示局部极小值的某些类似分形的行为。我们提供了一系列相互作用势，使得相关局部最小化器的支持没有孤立点，并且任何超水平集都没有内部点。
For the interaction energy with repulsive–attractive potentials, we give generic conditions which guarantee the radial symmetry of the local minimizers in the infinite Wasserstein distance. As a consequence, we obtain the uniqueness of local minimizers in this topology for a class of interaction potentials. We introduce a novel notion of concavity of the interaction potential allowing us to show certain fractal-like behavior of the local minimizers. We provide a family of interaction potentials such that the support of the associated local minimizers has no isolated points and any superlevel set has no interior points.