Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $C^1$, $C^2$, and weak type-$(1,1)$ estimates for linear elliptic
  operators   We show that any weak solution to elliptic equations in divergence form is
continuously differentiable provided that the modulus of continuity of
coefficients in the $L^1$-mean sense satisfies the Dini condition. This in
particular answers a question recently raised by Yanyan Li and allows us to
improve a result of Brezis. We also prove a weak type-$(1,1)$ estimate under a
stronger assumption on the modulus of continuity. The corresponding results for
non-divergence form equations are also established.

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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: physics
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
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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: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc