A remark on the Hadamard-Hirakawa formula for an electromagnetic cavity problem

In this paper we consider the eigenvalues of time-harmonic Maxwell’s equations in an electromagnetic cavity subject to a regular variation of the domain, described via a deformation function on the boundary. We show the direct equivalence of two Hadamard-type perturbation formulas for the shape deri...

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Bibliographic Details
Published inBollettino della Unione matematica italiana (2008) Vol. 17; no. 2; pp. 527 - 535
Main Author Zaccaron, Michele
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2024
Subjects
Mathematics
Mathematics and Statistics
Shape variations
Hadamard formula
35P15
Maxwell’s equations
Eigenvalue problem
35Q61
35Q60
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ISSN1972-6724
2198-2759
DOI10.1007/s40574-023-00380-w

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Summary:In this paper we consider the eigenvalues of time-harmonic Maxwell’s equations in an electromagnetic cavity subject to a regular variation of the domain, described via a deformation function on the boundary. We show the direct equivalence of two Hadamard-type perturbation formulas for the shape derivative of simple eigenvalues.
ISSN:1972-6724
2198-2759
DOI:10.1007/s40574-023-00380-w