Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A comparison principle for vector valued minimizers of semilinear
  elliptic energy, with application to dead cores   We establish a comparison principle providing accurate upper bounds for the
modulus of vector valued minimizers of an energy functional, associated when
the potential is smooth, to elliptic gradient systems. Our assumptions are very
mild: we assume that the potential is lower semicontinuous, and satisfies a
monotonicity condition in a neighborhood of its minimum. As a consequence, we
give a sufficient condition for the existence of dead core regions, where the
minimizer is equal to one of the minima of the potential.

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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol