A few results on permittivity variations in electromagnetic cavities
| Autor: | Paolo Luzzini, Michele Zaccaron |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Maxwell?s equations
Cavities Eigenvalue problem Permittivity variations Generic simplicity Applied Mathematics Mathematics::Spectral Theory Physics::Classical Physics Mathematics - Spectral Theory Mathematics - Analysis of PDEs 35Q61 35Q60 35P15 FOS: Mathematics Spectral Theory (math.SP) Analysis Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2202.00511 |
| Popis: | We study the eigenvalues of time-harmonic Maxwell's equations in a cavity upon changes in the electric permittivity $\varepsilon$ of the medium. We prove that all the eigenvalues, both simple and multiple, are locally Lipschitz continuous with respect to $\varepsilon$. Next, we show that simple eigenvalues and the symmetric functions of multiple eigenvalues depend real analytically upon $\varepsilon$ and we provide an explicit formula for their derivative in $\varepsilon$. As an application of these results, we show that for a generic permittivity all the Maxwell eigenvalues are simple. Comment: Added references and corrected some minor typos |
| Databáze: | OpenAIRE |
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