Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The extension problem for fractional Sobolev spaces with a partial
  vanishing trace condition   We construct whole-space extensions of functions in a fractional Sobolev
space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set
$O$ which vanish in a suitable sense on a portion $D$ of the boundary $\partial
O$ of $O$. The set $O$ is supposed to satisfy the so-called interior thickness
condition in $\partial O \setminus D$, which is much weaker than the global
interior thickness condition. The proof works by means of a reduction to the
case $D=\emptyset$ using a geometric construction.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph