Volume 29, 2023
|Number of page(s)||21|
|Published online||06 October 2023|
Whispering gallery modes for a transmission problem
Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay,
* Corresponding author: email@example.com
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  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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.