Original title: Geometric Versus Spectral Convergence for the Neumann Laplacian under Exterior Perturbations of the Domain
Authors: Arrieta, J. M. ; Krejčiřík, David
Document type: Papers
Conference/Event: 10th International Conference on Integral Methods in Science and Engineering, Santander (ES), 20080707
Year: 2010
Language: eng
Abstract: This chapter is concerned with the behavior of the eigenvalues and eigenfunctions of the Laplace operator in bounded domains when the domain undergoes a perturbation. It is well known that if the boundary condition that we are imposing is of Dirichlet type, the kind of perturbations that we may allow in order to obtain the continuity of the spectra is much broader than in the case of a Neumann boundary condition. This is explicitly stated in the pioneer work of Courant and Hilbert [CoHi53], and it has been subsequently clarified in many works, see [BaVy65, Ar97, Da03] and the references therein among others. See also [HeA06] for a general text on different properties of eigenvalues and [HeD05] for a study on the behavior of eigenvalues and in general partial differential equations when the domain is perturbed.
Keywords: Dirichlet condition; eigenvalues; Laplace operator
Host item entry: Integral Methods in Science and Engineering, ISBN 978-0-8176-4898-5

Institution: Nuclear Physics Institute AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0281537

Permalink: http://www.nusl.cz/ntk/nusl-373399


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