Linear stability analysis of overdetermined problems with non-constant data

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.3934/mine.2023048

Michiaki Onodera

引用次数: 2

Abstract

We study an overdetermined problem that arises as the Euler-Lagrange equation of a weighted variational problem in elasticity. Based on a detailed linear analysis by spherical harmonics, we prove the existence and local uniqueness as well as an optimal stability estimate for the shape of a domain allowing the solvability of the overdetermined problem. Our linear analysis reveals that the solution structure is strongly related to the choice of parameters in the problem. In particular, the global uniqueness holds for the pair of the parameters lying in a triangular region.

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非常数据超定问题的线性稳定性分析

研究了弹性力学中一个加权变分问题的欧拉-拉格朗日方程的超定问题。基于球面谐波的详细线性分析，我们证明了一个允许超定问题可解的区域形状的存在性、局部唯一性和最优稳定性估计。我们的线性分析表明，解的结构与问题中参数的选择密切相关。特别地，对于位于三角形区域的参数对，全局唯一性是成立的。

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.