Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schoenflies solutions of conformal boundary values may fail to be
  Sobolev   We show that there exists a planar Jordan domains $\Omega$ with boundary of
Hausdorff dimension $1$ such that, for any conformal maps $\varphi \colon
\mathbb D \to \Omega$, any homeomorphic extension of $\varphi$ or
$\varphi^{-1}$ to the entire plane is not in $W^{1,\,1}_{\rm loc}$ (or even not
in $BV_{\rm loc}$).

13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an