| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 75 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2023067 | |
| Published online | 06 October 2023 | |
Whispering gallery modes for a transmission problem
Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay,
Bâtiment 307,
91405
Orsay Cedex
France
* Corresponding author: spyridon.filippas@universite-paris-saclay.fr
Received:
8
February
2023
Accepted:
18
September
2023
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 [7] is optimal.
Mathematics Subject Classification: 35B60 / 47F05 / 93B07 / 35P20
Key words: Agmon estimates / eigenfunctions / transmission problem / wave propagation
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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