Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global regularity for a class of fully nonlinear PDEs with unbalanced
  variable degeneracy   We establish the existence and sharp global regularity results ($C^{0,
\gamma}$, $C^{0, 1}$ and $C^{1, \alpha}$ estimates) for a class of fully
nonlinear elliptic PDEs with unbalanced variable degeneracy. In a precise way,
the degeneracy law of the model switches between two different kinds of
degenerate elliptic operators of variable order, according to the null set of a
modulating function. Such sharp regularity estimates generalize and improve, to
some extent, earlier ones via geometric treatments. Our results are
consequences of geometric tangential methods and make use of compactness,
localized oscillating and scaling techniques. In the end, our findings are
applied in the study of a wide class of nonlinear models and free boundary
problems.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph