Singularity of eigenfunctions at the junction of shrinking tubes

Details Singularity of eigenfunctions at the junction of shrinking tubes Singularity of eigenfunctions at the junction of shrinking tubes

2012-02-20

arxiv.org/abs/1202.4414v1

Mathematics

Analysis of PDEs

48 pages

Scientific paper

Consider two domains connected by a thin tube: it can be shown that, generically, the mass of a given eigenfunction of the Dirichlet Laplacian concentrates in only one of them. The restriction to the other domain, when suitably normalized, develops a singularity at the junction of the tube, as the channel section tends to zero. Our main result states that, under a nondegeneracy condition, the normalized limiting profile has a singularity of order N-1, where N is the space dimension. We give a precise description of the asymptotic behavior of eigenfunctions at the singular junction, which provides us with some important information about its sign near the tunnel entrance. More precisely, the solution is shown to be one-sign in a neighborhood of the singular junction. In other words, we prove that the nodal set does not enter inside the channel.

Affiliated with

Also associated with

No associations

Rating

Singularity of eigenfunctions at the junction of shrinking tubes 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 Singularity of eigenfunctions at the junction of shrinking tubes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singularity of eigenfunctions at the junction of shrinking tubes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-565651