Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-adjoint and skew-symmetric extensions of the Laplacian with
  singular Robin boundary condition   We study the Laplacian in a smooth bounded domain, with a varying Robin
boundary condition singular at one point. The associated quadratic form is not
semi-bounded from below, and the corresponding Laplacian is not self-adjoint,
it has the residual spectrum covering the whole complex plane. We describe its
self-adjoint extensions and exhibit a physically relevant skew-symmetric one.
We approximate the boundary condition, giving rise to a family of self-adjoint
operators, and we describe their eigenvalues by the method of matched
asymptotic expansions. These eigenvalues acquire a strange behaviour when the
small perturbation parameter $\varepsilon>0$ tends to zero, namely they become
almost periodic in the logarithmic scale $|\ln \epsilon|$ and, in this way,
"wander" along the real axis at a speed $O(\eps^{-1})$.

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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol