Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improvement of flatness for vector valued free boundary problems   For a vectorial Bernoulli-type free boundary problem, with no sign assumption
on the components, we prove that flatness of the free boundary implies
$C^{1,\alpha}$ regularity, as well-known in the scalar case \cite{AC,C2}. While
in \cite{MTV2} the same result is obtained for minimizing solutions by using a
reduction to the scalar problem, and the NTA structure of the regular part of
the free boundary, our result uses directly a viscosity approach on the
vectorial problem, in the spirit of \cite{D}. We plan to use the approach
developed here in vectorial free boundary problems involving a fractional
Laplacian, as those treated in the scalar case in \cite{DR, DSS}.

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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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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: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics