Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On simple eigenvalues of the fractional Laplacian under removal of small
  fractional capacity sets   We consider the eigenvalue problem for the restricted fractional Laplacian in
a bounded domain with homogeneous Dirichlet boundary conditions. We introduce
the notion of fractional capacity for compact subsets, with the property that
the eigenvalues are not affected by the removal of zero fractional capacity
sets. Given a simple eigenvalue, we remove from the domain a family of compact
sets which are concentrating to a set of zero fractional capacity and we detect
the asymptotic expansion of the eigenvalue variation; this expansion depends on
the eigenfunction associated to the limit eigenvalue. Finally, we study the
case in which the family of compact sets is concentrating to a point.

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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas