Uniform stability in the Euclidean isoperimetric problem for the Allen–Cahn energy

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Francesco Maggi, Daniel Restrepo
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引用次数: 0

Abstract

We consider the isoperimetric problem defined on the whole n by the Allen–Cahn energy functional. For nondegenerate double-well potentials, we prove sharp quantitative stability inequalities of quadratic type which are uniform in the length scale of the phase transitions. We also derive a rigidity theorem for critical points analogous to the classical Alexandrov theorem for constant mean curvature boundaries.

艾伦-卡恩能量的欧几里得等周问题中的均匀稳定性
我们考虑了艾伦-卡恩能量函数在整个ℝn 上定义的等周问题。对于非enerate 双阱势,我们证明了二次型的尖锐定量稳定性不等式,这些不等式在相变的长度尺度上是均匀的。我们还推导出临界点的刚性定理,类似于恒定平均曲率边界的经典亚历山大定理。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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