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A Laplace operator with boundary conditions singular at one point

Marletta, Marco and Rozenblum, Grigori 2009. A Laplace operator with boundary conditions singular at one point. Journal of Physics A: Mathematical and Theoretical 42 (12) , 125204. 10.1088/1751-8113/42/12/125204

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Abstract

We discuss a recent paper of Berry and Dennis (J. Phys. A: Math. Theor. 2008 41 135203) concerning a Laplace operator on a smooth domain with singular boundary condition. We explain a paradox in the article (J. Phys. A: Math. Theor. 2008 41 135203) and show that if a certain additional condition is imposed, the result is a spectral problem for a self-adjoint operator having only eigenvalues and no continuous spectrum. The eigenvalues accumulate at ±∞ only, and we obtain the asymptotic behaviours of the counting functions n+(λ) and n−(λ) for positive and negative eigenvalues. The physical meaning of the additional boundary condition is not yet clear.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Publisher: IOP
ISSN: 1751-8113
Last Modified: 04 Jan 2019 21:02
URI: http://orca-mwe.cf.ac.uk/id/eprint/13969

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