Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev regularity of quasiconformal mappings on domains   Consider a Lipschitz domain $\Omega$ and a measurable function $\mu$
supported in $\overline\Omega$ with $\left\|{\mu}\right\|_{L^\infty}<1$. Then
the derivatives of a quasiconformal solution of the Beltrami equation
$\overline{\partial} f =\mu \partial f$ inherit the Sobolev regularity
$W^{n,p}(\Omega)$ of the Beltrami coefficient $\mu$ as long as $\Omega$ is
regular enough. The condition obtained is that the outward unit normal vector
$N$ of the boundary of the domain is in the trace space, that is, $N\in
B^{n-1/p}_{p,p}(\partial\Omega)$.

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The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga