Smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem.
type: Item
instance of: scholarly article
title: Smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem.
zbMATH Open document ID: 1040.49006
DOI: 10.1016/S0022-247X(02)00273-1
author: Jan Eisner
author: Lutz Recke
author: Milan Kučera
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The authors obtain interesting new results concerning continuation of solutions of variational inequalities depending on an eigenvalue parameter. The proof of the main result is based on an implicit function theorem applied to an equation which is equivalent to the variational inequality under consideration. As an application, the authors consider a class of elliptic equations of the type \(\triangle u(x)+\lambda(x)u(x)=\mu u(x)\) in \(\Omega\) with boundary conditions \(u=0\) on \(\Gamma_D,\;\partial u/\partial n=0\) on \(\partial\Omega\setminus (\Gamma_D\cup\Gamma_U),\;\int_{\Gamma_U} u\;d\Gamma\geq0,\;\partial u/\partial n\geq0\) on \(\Gamma_U,\;\partial u/\partial n\) is constant on \(\Gamma_U\) and \(\int_{\Gamma_U} u\;d\Gamma\cdot \partial u/\partial n=0\) on \(\Gamma_U\).
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35J85
zbMATH DE Number: 1866621
zbMATH Keywords: variational inequalities
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: continuation of solutions
zbMATH Keywords: unilateral conditions
reviewed by: Erich Miersemann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866621