Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dacorogna-Moser theorem on the Jacobian determinant equation with
  control of support   The original proof of Dacorogna-Moser theorem on the prescribed Jacobian PDE,
$\text{det}\,\nabla\varphi=f$, can be modified in order to obtain control of
support of the solutions from that of the initial data, while keeping optimal
regularity. Briefly, under the usual conditions, a solution diffeomorphism
$\varphi$ satisfying \[
\text{supp}(f-1)\subset\varOmega\Longrightarrow\text{supp}(\varphi-\text{id})\subset\varOmega
\] can be found and $\varphi$ is still of class $C^{r+1,\alpha}$ if $f$ is
$C^{r,\alpha}$, the domain of $f$ being a bounded connected open
$C^{r+2,\alpha}$ set $\varOmega\subset\mathbb{R}^{n}$.

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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: nlin