Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rectifiability and almost everywhere uniqueness of the blow-up for the
  vectorial Bernoulli free boundaries   We prove that for minimizers of the vectorial Alt-Caffarelli functional the
two-phase singular set of the free boundary is rectifiable and the blow-up is
unique almost everywhere on it. While the first conclusion is an application of
the recent techniques developed by Naber and Valtorta, the uniqueness part
follows from the rectifiability and a new application of the
Alt-Caffarelli-Friedman monotonicity formula.

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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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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: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int