Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity versus singularities for elliptic problems in two dimensions   In two dimensions every weak solution to a nonlinear elliptic system
$\rm{div} a(x,u,Du)=0$ has H\"older continuous first derivatives provided that
standard continuity, ellipticity and growth assumptions hold with a growth
exponent $p \geq 2$. We give an example showing that this result cannot be
extended to the subquadratic case, i.e. that weak solutions are not necessarily
continuous if $1< p <2$. Furthermore, we discuss related results for
variational integrals.

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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol