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...

Full description

Saved in:
Bibliographic Details
Published inMathematics in engineering Vol. 5; no. 1; pp. 1 - 31
Main Authors Lamberti, Pier Domenico, Zaccaron, Michele
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
boundary homogenization
cavities
maxwell's equations
shape sensitivity
spectral stability
Online AccessGet full text
ISSN2640-3501
2640-3501
DOI10.3934/mine.2023018

Cover

More Information
Summary: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.
ISSN:2640-3501
2640-3501
DOI:10.3934/mine.2023018