Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral analysis of the biharmonic operator subject to Neumann boundary
  conditions on dumbbell domains   We consider the biharmonic operator subject to homogeneous boundary
conditions of Neumann type on a planar dumbbell domain which consists of two
disjoint domains connected by a thin channel. We analyse the spectral behaviour
of the operator, characterizing the limit of the eigenvalues and of the
eigenprojections as the thickness of the channel goes to zero. In applications
to linear elasticity, the fourth order operator under consideration is related
to the deformation of a free elastic plate, a part of which shrinks to a
segment. In contrast to what happens with the classical second order case, it
turns out that the limiting equation is here distorted by a strange factor
depending on a parameter which plays the role of the Poisson coefficient of the
represented plate.

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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph