An alternative derivation of the eigenvalue equation for the 1-Laplace operator
type: Item
instance of: scholarly article
title: An alternative derivation of the eigenvalue equation for the 1-Laplace operator
zbMATH Open document ID: 1113.47053
author: Friedemann Schuricht
published in: Archiv der Mathematik
publication date: 2007-02-14T00:00:00Z
review text: The purpose of this paper is to provide an alternative simpler derivation of the eigenvalue equation for the 1-Laplace operator. Minimizers of the total variation subject to a prescribed \(\mathcal L^1\)-norm are considered as eigensolutions of the 1-Laplace operator. The derivation of the corresponding eigenvalue equation, which requires particular care due to the lack of smoothness, was carried out in [\textit{B.\,Kawohl} and \textit{F.\,Schuricht}, ``Dirichlet problems for the 1-Laplace operator, including the eigenvalue problem'', Commun.\ Contemp.\ Math.\ (to appear)] by using particular methods of nonsmooth analysis. The paper under review provides a simpler proof that exploits the special structure of the problem.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 47J10
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49K22
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 5126582
zbMATH Keywords: eigenvalue equation
zbMATH Keywords: eigensolution
zbMATH Keywords: 1-Laplace operator
zbMATH Keywords: minimising problem
MaRDI profile type: Publication
full work available at URL: s00013-006-1827-2
OpenAlex ID: W2027980600
DOI: 10.1007/S00013-006-1827-2
description: scientific article; zbMATH DE number 5126582