Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy estimates for minimizers to a class of elliptic systems of
  Allen-Cahn type and the Liouville property   We prove a theorem for the growth of the energy of bounded, globally
minimizing solutions to a class of semilinear elliptic systems of the form
$\Delta u=\nabla W(u)$, $x\in \mathbb{R}^n$, $n\geq 2$, with $W:\mathbb{R}^m\to
\mathbb{R}$, $m\geq 1$, nonnegative and vanishing at exactly one point (at
least in the closure of the image of the considered solution $u$). As an
application, we can prove a Liouville type theorem under various assumptions.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: stat