Sharp bounds for ground state eigenfunctions on domains with Horns and cusps
type: Item
instance of: scholarly article
title: Sharp bounds for ground state eigenfunctions on domains with Horns and cusps
zbMATH Open document ID: 0889.35071
author: M. M. H. Pang
author: Arthur II Lindeman
author: Z. Zhao
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-06-18T00:00:00Z
review text: The authors consider the first eigenfunction of the Laplacian under Dirichlet boundary conditions for special ``horn shaped'' domains \(\Omega\): a) \(\Omega_p =\{(x,y) \in \mathbb{R} \times \mathbb{R}^{N-1};\;x>0,\;|y|<\rho(x)\}\), where \(\rho(x) \downarrow 0\) for \(x\to \infty\), \(\rho\in C'[0, \infty)\), \(\lim_{x\to\infty} |\rho' |=0\). b) The finite case: \(\Omega_\nu =\{(x,y) \in\mathbb{R} \times \mathbb{R}^{N-1}\), \(0<x<1\), \(|y|<\nu(x)\}\), where \(\nu(x) \downarrow 0\) for \(x\to 0\) and \(\lim_{x\to 0} |\nu' |=0\). They then prove lower bounds for the first eigenfunction \(\varphi(x)\) of \(\Omega\) in terms of the first eigenfunction of the unit ball of \(\mathbb{R}^{N-1}\).
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1053991
zbMATH Keywords: horn shaped domains
zbMATH Keywords: first eigenfunction
reviewed by: René Sperb
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5508
OpenAlex ID: W2010047796
cites work: Sharp estimates for Dirichlet eigenfunctions in simply connected domains
cites work: Q5287470
cites work: Dirichlet Eigenfunctions for Horn-Shaped Regions and Laplacians on Cross Sections
cites work: Sharp estimates for Dirichlet eigenfunctions in horn-shaped regions
cites work: Erratum: Sharp estimates for Dirichlet eigenfunctions in Horn-shaped regions
cites work: A boundary Harnack principle in twisted Hölder domains
cites work: Eigenfunction and harmonic function estimates in domains with horns and cusps
cites work: Q4041031
cites work: Heat Kernel Bounds for Second Order Elliptic Operators on Riemannian Manifolds
cites work: Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
cites work: Q3771199
DOI: 10.1006/JMAA.1997.5508
description: scientific article; zbMATH DE number 1053991