Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace and extension theorems for functions of bounded variation   In this paper we show that every $L^1$-integrable function on
$\partial\Omega$ can be obtained as the trace of a function of bounded
variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary
$\partial\Omega$ in a doubling metric measure space. In particular, the trace
class of $BV(\Omega)$ is $L^1(\partial\Omega)$ provided that $\Omega$ supports
a 1-Poincar\'e inequality. We also construct a bounded linear extension from a
Besov class of functions on $\partial\Omega$ to $BV(\Omega)$.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph