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Shape sensitivity analysis for electromagnetic cavities
  • Pier Domenico Lamberti,
  • Michele Zaccaron
Pier Domenico Lamberti
Università degli Studi di Padova
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Michele Zaccaron
Università degli Studi di Padova
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Abstract

We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of the elementary symmetric functions of the eigenvalues splitting a multiple eigenvalue, as well as a Rellich-Nagy-type result describing the corresponding bifurcation phenomenon. We also address an isoperimetric problem and characterize the critical cavities for the symmetric functions of the eigenvalues subject to isovolumetric or isoperimetric domain perturbations and prove that balls are critical. We include known formulas for the eigenpairs in a ball and calculate the first one.

Peer review status:ACCEPTED

23 Apr 2020Submitted to Mathematical Methods in the Applied Sciences
25 Apr 2020Submission Checks Completed
25 Apr 2020Assigned to Editor
29 Apr 2020Reviewer(s) Assigned
15 Mar 2021Review(s) Completed, Editorial Evaluation Pending
15 Mar 2021Editorial Decision: Revise Minor
20 Mar 20211st Revision Received
20 Mar 2021Submission Checks Completed
20 Mar 2021Assigned to Editor
20 Mar 2021Editorial Decision: Accept