Some spectral properties of Rooms and Passages domains and their skeletons

Autor:	Brown, B. M., Evans, W. D., Wood, I. G.
Rok vydání:	2013
Předmět:	Mathematics - Spectral Theory Mathematics - Analysis of PDEs 35P20 47F05
Druh dokumentu:	Working Paper
Popis:	In this paper we investigate spectral properties of Lapla- cians on Rooms and Passages domains. In the first part, we use Dirichlet- Neumann bracketing techniques to show that for the Neumann Lapla- cian in certain Rooms and Passages domains the second term of the asymptotic expansion of the counting function is of order $\sqrt{\lambda}$. For the Dirichlet Laplacian our methods only give an upper estimate of the form $\sqrt{\lambda}$. In the second part of the paper, we consider the relation- ship between Neumann Laplacians on Rooms and Passages domains and Sturm-Liouville operators on the skeleton. Comment: 19 pages, 6 figures, to appear in Proceedings of Symposia in Pure Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1301.4396 Zobrazit plný text záznamu View this record from Arxiv