论文标题
具有竞争非本地单数术语的等速度问题
An isoperimetric problem with a competing nonlocal singular term
论文作者
论文摘要
在本文中，我们研究了通常的外围与非本地奇异项竞争的功能的最小化，在该功能中，可比较（但不一定等于）分数周长。这个问题的动机是第一作者在先前的某些工作中引入的细胞运动模型。我们建立了有关具有数量限制的全球最小化器的几个事实。特别是，我们证明了最小化器存在，并且对小质量是径向对称的，而最小化的人不能在大质量上径向对称。对于大质量，我们证明，最小化序列要么分成较小的集合，这些序列会漂移到无穷大，要么形成了处方宽度的手指。最后，我们将这两种替代方案连接到相关的最小化问题，以使经典插值不平等（Gagliardo-nirenberg类型的分数外围）中的最佳常数连接起来。
In this paper, we investigate the minimization of a functional in which the usual perimeter is competing with a nonlocal singular term comparable (but not necessarily equal to) a fractional perimeter. The motivation for this problem is a cell motility model introduced in some previous work by the first author. We establish several facts about global minimizers with a volume constraint. In particular we prove that minimizers exist and are radially symmetric for small mass, while minimizers cannot be radially symmetric for large mass. For large mass, we prove that the minimizing sequences either split into smaller sets that drift to infinity or develop fingers of a prescribed width. Finally, we connect these two alternatives to a related minimization problem for the optimal constant in a classical interpolation inequality (a Gagliardo-Nirenberg type inequality for fractional perimeter).
