Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dirichlet problem for the Jacobian equation in critical and
  supercritical Sobolev spaces   We study existence and regularity of solutions to the Dirichlet problem for
the prescribed Jacobian equation, $\det Du = f$, where $f$ is integrable and
bounded away from zero. In particular, we take $f\in L^p$, where $p > 1$, or in
$L\log L$. We prove that for a Baire-generic $f$ in either space there are no
solutions with the expected regularity.

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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th