Localization of eigenfunctions in a thin domain with locally periodic oscillating boundary

2020/04/15 by Klas Pettersson, Pettersson, Klas
Computer Science · Mathematics · #35B25 #35B27 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2004.07023

openalex publication_date 2020/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a Dirichlet spectral problem for a second-order elliptic operator with locally periodic coefficients in a thin domain. The boundary of the domain is assumed to be locally periodic. When the thickness of the domain ε tends to zero, the eigenvalues are of order ε^-2 and described in terms of the first eigenvalue μ(x₁) of an auxiliary spectral cell problem parametrized by x₁, while the eigenfunctions localize with rate √(ε).

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