Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some remarks on the Lp regularity of second derivatives of solutions to
  non-divergence elliptic equations and the Dini condition   In this note we prove an end-point regularity result on the Lp integrability
of the second derivatives of solutions to non-divergence form uniformly
elliptic equations whose second derivatives are a priori only known to be
integrable. The main assumption on the elliptic operator is the Dini continuity
of the coefficients. We provide a counterexample showing that the Dini
condition is somehow optimal. We also give a counterexample related to the BMO
regularity of second derivatives of solutions to elliptic equations.

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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin