Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On higher integrability estimates for elliptic equations with singular
  coefficients   In this note we establish existence and uniqueness of weak solutions of
linear elliptic equation $\text{div}[\mathbf{A}(x) \nabla u] =
\text{div}{\mathbf{F}(x)}$, where the matrix $\mathbf{A}$ is just measurable
and its skew-symmetric part can be unbounded. Global reverse H\"{o}lder's
regularity estimates for gradients of weak solutions are also obtained. Most
importantly, we show, by providing an example, that boundedness and ellipticity
of $\mathbf{A}$ is not sufficient for higher integrability estimates even when
the symmetric part of $\mathbf{A}$ is the identity matrix. In addition, the
example also shows the necessity of the dependence of $\alpha$ in the
H\"{o}lder $C^\alpha$-regularity theory on the \textup{BMO}-semi norm of the
skew-symmetric part of $\mathbf{A}$. The paper is an extension of classical
results obtained by N. G. Meyers (1963) in which the skew-symmetric part of
$\mathbf{A}$ is assumed to be zero.

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The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: atom-ph