Geometric Versus Spectral Convergence for the Neumann Laplacian under Exterior Perturbations of the Domain

0486817 - ÚJF 2018 US eng C - Konferenční příspěvek (zahraniční konf.)
Arrieta, J. M. - Krejčiřík, David
Geometric Versus Spectral Convergence for the Neumann Laplacian under Exterior Perturbations of the Domain.
Integral Methods in Science and Engineering. Vol. 1. Cambridge: Springer, 2010, s. 9-19. ISBN 978-0-8176-4898-5.
[10th International Conference on Integral Methods in Science and Engineering. Santander (ES), 07.07.2008-10.07.2008]
Institucionální podpora: RVO:61389005
Klíčová slova: eigenvalues * Laplace operator * Dirichlet condition
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

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.
Trvalý link: http://hdl.handle.net/11104/0281537