Whispering gallery modes for a transmission problem

2023/02/10 by Spyridon Filippas, Filippas, Spyridon · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2302.05215

openalex publication_date 2023/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Variational data assimilation for the wave equation in heterogeneous media: Numerical investigation of stability
• Cauchy Data for 1D singular Schrödinger operators

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