An alternative derivation of the eigenvalue equation for the 1-Laplace operator
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.
scientific article; zbMATH DE number 5126582