Eigenvalues of the Laplace-Beltrami operator on a large spherical cap under the Robin problem
type: Item
instance of: scholarly article
title: Eigenvalues of the Laplace-Beltrami operator on a large spherical cap under the Robin problem
zbMATH Open document ID: 1317.35152
author: Yoshitsugu Kabeya
author: Tatsuki Kawakami
author: Atsushi Kosaka
author: Hirokazu Ninomiya
published in: Kodai Mathematical Journal
publication date: 2015-01-19T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kmj/1414674613
review text: This paper studies the linear eigenvalue problem \[ \Lambda v+\lambda v=0\quad \text{in } \Omega_\epsilon \subset S^n, \] \[ (\cos \sigma )\partial_n v+(\sin \sigma )v=0\quad \text{on } \partial \Omega_\epsilon, \] where \(\Lambda \) is the Laplace-Beltrami operator on the unit sphere \(S^n \subset R^{n+1}\) for \(n\geq 2\), \(\Omega_\epsilon \) is the spherical cap centered at the north pole \((0,0,\dots,0,1)\) of its geodesic radius \(\pi -\epsilon \) with \(\epsilon >0\), \(\partial_n\) is the derivative of the outer unit normal to \(\Omega_\epsilon \) and \(\sigma \in [0,\pi /2]\), \(\lambda >0\) are parameters. The behaviour of the eigenvalues of \(-\Lambda \) as \(\epsilon \to 0_+\) is studied.
reviewed by: Dagmar Medková
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 33C55
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 6387908
zbMATH Keywords: spherical cap
zbMATH Keywords: eigenvalues
zbMATH Keywords: associated Legendre functions
MaRDI profile type: Publication
OpenAlex ID: W1991799830
DOI: 10.2996/KMJ/1414674613
description: scientific article; zbMATH DE number 6387908