A Rellich type theorem for the Helmholtz equation in a conical domain
Résumé
We prove that there cannot exist square-integrable nonzero solutions to the Helmholtz equation in an axisymmetric conical domain whose vertex angle is greater than π. This implies in particular the absence of eigenvalues embedded in the essential spectrum of a large class of partial differential operators which coincide with the Laplacian in the conical domain.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
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