Estimates for Resonant Frequencies Under Boundary Deformation in Multi-dimensional Space

Abdessatar Khelifi, Mohammed Nour Shamma

Abstract

In multi-dimensional space, we address the
integral equation method to investigate the interplay between the geometry, boundary conditions and the properties of the resonant
frequencies and their associated eigenfunctions under boundary variations of domain. We provide a rigorous derivation of asymptotic
expansions for eigenfunctions and we establish error estimations for both resonant frequencies and eigenfunctions of the Helmholtz
eigenvalue problem.

Keywords

Resonant frequencies, Boundary integral equation, Error estimates

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