Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An anisotropic monotoncity formula, with applications to some
  segregation problems   We prove an Alt-Caffarelli-Friedman montonicity formula for pairs of
functions solving elliptic equations driven by different ellipticity matrices
in their positivity sets. As application, we derive Liouville-type theorems for
subsolutions of some elliptic systems, and we analyze segregation phenomena for
systems of equations where the diffusion of each density is described by a
different operator.

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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-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
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: physics