扰动电磁腔上基于一致Gaffney不等式的curlcurl算子的谱稳定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-30 DOI:10.3934/mine.2023018

P. D. Lamberti, Michele Zaccaron

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引用次数: 3

摘要

我们证明了在边界扰动下腔上的$ curl $算子在电边界条件下的谱稳定性结果。假设空腔是足够光滑的，但我们对扰动的强度施加了微弱的限制。这些方法是变分型的，基于两个主要成分:在域之间构造合适的piola型变换和用Dirichlet Laplacian泊松问题的一致先验$ H^2 $估计得到的一致Gaffney不等式的证明。利用V. Maz'ya和T. Shaposhnikova基于Sobolev乘子的结果证明了均匀先验估计。还指出了与边界均匀化问题的联系。

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Spectral stability of the curlcurl operator via uniform Gaffney inequalities on perturbed electromagnetic cavities

We prove spectral stability results for the $ curl curl $ operator subject to electric boundary conditions on a cavity upon boundary perturbations. The cavities are assumed to be sufficiently smooth but we impose weak restrictions on the strength of the perturbations. The methods are of variational type and are based on two main ingredients: the construction of suitable Piola-type transformations between domains and the proof of uniform Gaffney inequalities obtained by means of uniform a priori $ H^2 $-estimates for the Poisson problem of the Dirichlet Laplacian. The uniform a priori estimates are proved by using the results of V. Maz'ya and T. Shaposhnikova based on Sobolev multipliers. Connections to boundary homogenization problems are also indicated.

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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.