Spectral stability of the curlcurl operator via uniform Gaffney inequalities on perturbed electromagnetic cavities
We prove spectral stability results for the curlcurl 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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Institute of Mathematical Sciences
2023
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| Subjects: | |
| Online Access: | View Fulltext in Publisher |
| Summary: | We prove spectral stability results for the curlcurl 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 H2-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. c 2023 the Author(s), |
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| ISBN: | 26403501 (ISSN) |
| DOI: | 10.3934/mine.2023018 |