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arXiv · 1301.4396

Some spectral properties of Rooms and Passages domains and their skeletons

B. M. Brown·W. D. Evans·I. G. Wood
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Abstract

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 $\sqrtλ$. For the Dirichlet Laplacian our methods only give an upper estimate of the form $\sqrtλ$. 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.

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B. M. Brown, W. D. Evans, I. G. Wood. 2013-01-18. Some spectral properties of Rooms and Passages domains and their skeletons. https://arxiv.org/abs/1301.4396

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