As is well known, by the Floquet-Bloch theory for periodic problems, one can transform a spectral Laplace-Dirichlet problem in the plane with a set of periodic perforations into a family of "model problems" depending on a parameter eta is an element of[0, 2 pi](2) for quasiperiodic functions in the unit cell with a single perforation. We prove real analyticity results for the eigenvalues of the model problems upon perturbation of the shape of the perforation of the unit cell.
A REAL ANALYTICITY RESULT FOR SYMMETRIC FUNCTIONS OF THE EIGENVALUES OF A QUASIPERIODIC SPECTRAL PROBLEM FOR THE DIRICHLET LAPLACIAN
Lanza de Cristoforis M.
Writing – Original Draft Preparation
;Musolino P.Writing – Original Draft Preparation
;
2021
Abstract
As is well known, by the Floquet-Bloch theory for periodic problems, one can transform a spectral Laplace-Dirichlet problem in the plane with a set of periodic perforations into a family of "model problems" depending on a parameter eta is an element of[0, 2 pi](2) for quasiperiodic functions in the unit cell with a single perforation. We prove real analyticity results for the eigenvalues of the model problems upon perturbation of the shape of the perforation of the unit cell.
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