Whispering gallery modes for a transmission problem
Analysis of PDEs
2023-02-13 v1 Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2302.05215,
title = {Whispering gallery modes for a transmission problem},
author = {Spyridon Filippas},
journal= {arXiv preprint arXiv:2302.05215},
year = {2023}
}