On the first Steklov-Dirichlet eigenvalue on eccentric annuli in general dimensions

2023/09/18 by Jiho Hong, Mikyoung Lim, Hong, Jiho +3
Computer Science · Mathematics · #35P15 #42C10 #49R05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2309.09587

openalex publication_date 2023/09/18 · openalex created_date 2023/09/20 · openalex updated_date 2026/07/28

Abstract

We consider the Steklov-Dirichlet eigenvalue problem on eccentric annuli in Euclidean space of general dimensions. In recent work by the same authors of this paper [21], a limiting behavior of the first eigenvalue, as the distance between the two boundary circles of an annulus approaches zero, was obtained in two dimensions. We extend this limiting behavior to general dimensions by employing bispherical coordinates and expressing the first eigenfunction as a Fourier-Gegenbauer series.

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