Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized elastica problems under area constraint   It was recently proved that the elastic energy
$E(\gamma)=\tfrac{1}{2}\int_\gamma\kappa^2 ds$ of a closed curve $\gamma$ with
curvature $\kappa$ has a minimizer among all plane, simple, regular and closed
curves of given enclosed area $A(\gamma)$, and that the minimum is attained
only for circles. Here we show under which hypothesis the result can be
extended to other functionals involving the curvature. As an example we show
that the optimal shape remains a circle for the $p$-elastic energy
$\int_\gamma|\kappa|^p ds$, whenever $p>1$.

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The categories of this paper are: stat
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The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg