Stable anisotropic capillary hypersurfaces in a wedge

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.3934/mine.2023029

Miyuki Koiso

引用次数: 3

Abstract

We study a variational problem for hypersurfaces in a wedge in the Euclidean space. Our wedge is bounded by a finitely many hyperplanes passing a common point. The total energy of each hypersurface is the sum of its anisotropic surface energy and the wetting energy of the planar domain bounded by the boundary of the considered hypersurface. An anisotropic surface energy is a generalization of the surface area which was introduced to model the surface tension of a small crystal. We show an existence and uniqueness result of local minimizers of the total energy among hypersurfaces enclosing the same volume. Our result is new even when the special case where the surface energy is the surface area.

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楔体中稳定的各向异性毛细超表面

研究了欧几里德空间中楔形超曲面的一个变分问题。我们的楔形被有限多个超平面包围，这些超平面经过一个公共点。每个超表面的总能量是其各向异性表面能和被考虑的超表面边界包围的平面域的润湿能的总和。各向异性表面能是对表面积的一般化，它被引入到小晶体的表面张力模型中。给出了围成相同体积的超曲面间总能量局部极小值的存在唯一性结果。即使在表面能等于表面积的特殊情况下，我们的结果也是新的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

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.