Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev homeomorphic extensions   Let $\mathbb X$ and $\mathbb Y$ be $\ell$-connected Jordan domains, $\ell \in
\mathbb N$, with rectifiable boundaries in the complex plane. We prove that any
boundary homeomorphism $\varphi \colon \partial \mathbb X \to \partial \mathbb
Y$ admits a Sobolev homeomorphic extension $h \colon \overline{\mathbb X} \to
\overline{\mathbb Y}$ in $W^{1,1} (\mathbb X, \mathbb C)$. If instead $\mathbb
X$ has $s$-hyperbolic growth with $s>p-1$, we show the existence of such an
extension lies in the Sobolev class $W^{1,p} (\mathbb X, \mathbb C)$ for $p\in
(1,2)$. Our examples show that the assumptions of rectifiable boundary and
hyperbolic growth cannot be relaxed. We also consider the existence of
$W^{1,2}$-homeomorphic extensions subject to a given boundary data.

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The categories of this paper are: nlin
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
1
The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn