On the first and second variations of a nonlocal isoperimetric problem
On the first and second variations of a nonlocal isoperimetric problem
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DOI：
10.1515/crelle.2007.074
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发表时间：
2007-01
期刊：
影响因子：
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通讯作者：
Rustum Choksi;P. Sternberg
中科院分区：
文献类型：
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作者：
Rustum Choksi;P. Sternberg
考虑一类等周变分问题的非局部扰动。这个问题可以被看作是一个数学范式的无处不在的现象，能源驱动的模式形成与竞争的短期和长期的相互作用。特别地，它作为用于二嵌段共聚物的微相分离的模型的Γ-极限而出现。在本文中，我们建立了临界性和稳定性的精确条件（即我们明确计算第一和第二变分）。我们还介绍了一些应用。
We consider a nonlocal perturbation of an isoperimetric variational problem. The problem may be viewed as a mathematical paradigm for the ubiquitous phenomenon of energy-driven pattern formation associated with competing short and long-range interactions. In particular, it arises as a Γ-limit of a model for microphase separation of diblock copolymers. In this article, we establish precise conditions for criticality and stability (i.e. we explicitly compute the first and second variations). We also present some applications.