Estimates for the first eigenfunction of linear eigenvalue problems via Steiner symmetrization
type: Item
instance of: scholarly article
title: Estimates for the first eigenfunction of linear eigenvalue problems via Steiner symmetrization
zbMATH Open document ID: 1173.35089
DOI: 10.5565/PUBLMAT_53109_02
author: Francesco Chiacchio
published in: Publicacions Matemàtiques
publication date: 2009-01-29T00:00:00Z
full work available at URL: https://eudml.org/doc/42272
review text: The paper deals with the fixed membrane problem \[ \Delta u+\lambda u=0 \quad\text{in } D, \qquad u=0 \quad\text{on }\partial D, \] where \(D\) is a bounded domain of \(\mathbb R^n\). It is well-known that Schwarz symmetrization allowed to obtain estimates for the first eigenfunction and for the eigenvalues \(\lambda_i\) of the problem under consideration. \textit{G. Chiti} [Boll. Unione Mat. Ital., VI. Ser., A 1, 145--151 (1982; Zbl 0484.35067)] proved pointwise estimations for the Schwarz rearrangement of \(u\). Basing on Chiti's result the author gives estimates for the first eigenfunction which are sharper than the results given in the above mentioned paper. The paper contains also an extension to a class of more general elliptic problems.
reviewed by: Bodo Dittmar
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5500101
zbMATH Keywords: Steiner symmetrization
zbMATH Keywords: fixed membrane problem
zbMATH Keywords: linear eigenvalue problems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5500101