Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates of the best Sobolev constant of the embedding of $BV(\Omega)$
  into $L^1(\partial\Omega)$ and related shape optimization problems   In this paper we find estimates for the optimal constant in the critical
Sobolev trace inequality $\lambda_1(\Omega)\|u\|_{L^1(\partial\Omega)} \le
\|u\|_{W^{1,1}(\Omega)}$ that are independent of $\Omega$. This estimates
generalize those of \cite{BS} concerning the $p$-Laplacian to the case $p=1$.
  We apply our results to prove existence of an extremal for this embedding. We
then study an optimal design problem related to $\lambda_1$, and eventually
compute the shape derivative of the functional $\Omega\to\lambda_1(\Omega)$. As
a consequence, we obtain that a ball of $\R^n$ of radius $n$ is critical for
volume-preserving deformations.

10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con