Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elimination of Hamilton-Jacobi equation in extreme variational problems   It is shown that extreme problem for one-dimensional Euler-Lagrange
variational functional in $C^1[a;b]$ under the strengthened Legendre condition
can be solved without using Hamilton-Jacobi equation. In this case, exactly one
of the two possible cases requires a restriction to a length of $[a;b]$,
defined only by the form of integrand. The result is extended to the case of
compact extremum in $H^1[a;b]$.

14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph