Whispering gallery modes for a transmission problem
Résumé
We construct a specific family of eigenfunctions for a Laplace operator with coefficients having a jump across an interface. These eigenfunctions have an exponential concentration arbitrarily close to the interface, and therefore could be considered as whispering gallery modes. The proof is based on an appropriate Agmon estimate. We deduce as a corollary that the quantitative unique continuation result for waves propagating in singular media proved by the author in [Fil22] is optimal.
Mots clés
Agmon estimates eigenfunctions transmission problem wave propagation 2010 Mathematics Subject Classification: 35B60 47F05 93B07 35P20
Agmon estimates
eigenfunctions
transmission problem
wave propagation 2010 Mathematics Subject Classification: 35B60
47F05
93B07
35P20
Agmon estimates eigenfunctions transmission problem wave propagation 2010 Mathematics Subject Classification: 35B60 47F05 93B07 35P20
Origine | Fichiers produits par l'(les) auteur(s) |
---|