Asymptotic property of eigenfunction of the Laplacian at the boundary
type: Item
instance of: scholarly article
title: Asymptotic property of eigenfunction of the Laplacian at the boundary
zbMATH Open document ID: 0808.35090
author: Shin Ozawa
published in: Osaka Journal of Mathematics
publication date: 1994-07-07T00:00:00Z
review text: Let \(M\) be a bounded region in \(\mathbb{R}^ n\) with smooth boundary, \(\lambda_ j\) the \(j\)-th eigenvalue and \(\{\varphi_ j\): \(j\in\mathbb{N}\}\) a complete orthogonal basis of eigenfunctions of \(-\Delta\) in \(M\) under Dirichlet condition. Then \[ \sum_{k=0}^ \infty e^{-\lambda_ j t} \partial_ \nu \varphi_ j(x)^ 2\sim \sum_{j=1}^ \infty C_ k(x) t^{{{k-n-3} \over 2}} \] holds when \(t\to 0\). The author also gives some conjectures and problems.
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 579224
zbMATH Keywords: asymptotic of eigenfunctions
zbMATH Keywords: Dirichlet condition
reviewed by: Gianfranco Bottaro
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 579224