Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inequality \`a la Szeg\H{o}-Weinberger for the $p-$Laplacian on
  convex sets   In this paper we prove a sharp inequality of Szeg\H{o}-Weinberger type for
the first nontrivial eigenvalue of the $p-$Laplacian with Neumann boundary
conditions. This applies to convex sets with given diameter. Some variants,
extensions and limit cases are investigated as well.

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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: physics