Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Properties of the Neumann-Laplace operator in Quasiconformal
  Regular Domains   In this paper we study spectral properties of the Neumann-Laplace operator in
planar quasiconformal regular domains $\Omega\subset\mathbb R^2$. This study is
based on the quasiconformal theory of composition operators on Sobolev spaces.
Using the composition operators theory we obtain estimates of constants in
Poincar\'e-Sobolev inequalities and as a consequence lower estimates of the
first non-trivial eigenvalue of the Neumann-Laplace operator in planar
quasiconformal regular domains.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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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: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con