Mathematics – Spectral Theory
Scientific paper
2009-01-29
Integral Methods in Science and Engineering, vol. 1, pp. 9-19, Birkhauser, Boston, 2009
Mathematics
Spectral Theory
11 pages, LaTeX with 1 EPS figure
Scientific paper
We analyze the behavior of the eigenvalues and eigenfunctions of the Laplace operator with homogeneous Neumann boundary conditions when the domain is perturbed. We focus on exterior perturbations of the domain, that is, the limit domain is contained in each of the perturbed domains. Moreover, the family of perturbed domains is made up of bounded domains although not necessarily uniformly bounded. We show that if we know that the eigenvalues and eigenfunctions of the perturbed domains converge to the ones of the limit domain, then necessarily we have that the measure of the perturbation tends to zero, while it is not necessarily true for the Hausdorff distance of the perturbation. As a matter of fact we will construct an example of a perturbation where the spectra behave continuously but the distance tends to infinity.
Arrieta Jose M.
Krejcirik David
No associations
LandOfFree
Geometric versus spectral convergence for the Neumann Laplacian under exterior perturbations of the domain does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Geometric versus spectral convergence for the Neumann Laplacian under exterior perturbations of the domain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric versus spectral convergence for the Neumann Laplacian under exterior perturbations of the domain will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-13915