Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schauder estimates for solutions of sub-Laplace equations with Dini
  terms   In this paper we establish Schauder estimates for the sublalpace equation
\[\Sigma_{j = 1}^mX_j^2u = f,\] where ${X_1},{X_2}, \ldots ,{X_m}$ is a system
of smooth vector field which generates the first layer in the Lie algebra of a
Carnot group. We drive the estimate for the second order derivatives of the
solution to the equation with Dini continue inhomogeneous term $f$ by the
perturbation argument.

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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg