Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^{1, \alpha}$ Regularity for degenerate fully nonlinear elliptic
  equations with Neumann boundary conditions   In this paper, we establish $C^{1, \alpha}$ regularity upto the boundary for
a class of degenerate fully nonlinear elliptic equations with Neumann boundary
conditions. Our main result Theorem 2.1 constitutes the boundary analogue of
the interior $C^{1, \alpha}$ regularity result established in [21] for
equations with similar structural assumptions. The proof of our main result is
achieved via compactness arguments combined with new boundary H\"{o}lder
estimates for equations which are uniformly elliptic when the gradient is
either small or large.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin