TY  - JOUR
AU  - Lamberti, Pier Domenico
AU  - Zaccaron, Michele
PY  - 2023
TI  - Spectral stability of the curlcurl operator via uniform Gaffney inequalities on perturbed electromagnetic cavities
JO  - Mathematics in Engineering
SP  - 1
EP  - 31
VL  - 5
IS  - 1
AB  - 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.
UR  - https://doi.org/10.3934/mine.2023018
DO  - 10.3934/mine.2023018