Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euler's optimal profile problem   We study an old variational problem formulated by Euler as Proposition 53 of
his `Scientia Navalis' by means of the direct method of the calculus of
variations. Precisely, through relaxation arguments, we prove the existence of
minimizers. We fully investigate the analytical structure of the minimizers in
dependence of the geometric parameters and we identify the ranges of uniqueness
and non-uniqueness.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: stat