Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Starshape of the superlevel sets of solutions to equations involving the
  fractional Laplacian in starshaped rings   In the present work we study solutions of the problem $-(-\Delta)^{\alpha/2}u
= f(x,u)$ in $D_0\setminus \overline{D}_1$, with exterior conditions $u = 0$ in
$R^N \setminus D_0$ and $u = 1$ in $\overline{D}_1$, where $D_1, D_0 \subset
R^N$ are open sets such that $\overline{D}_1 \subset D_0$, $\alpha \in (0,2)$,
and $f$ is a nonlinearity. Under different assumptions on $f$ we prove that, if
$D_0$ and $D_1$ are starshaped with respect to the same point $\bar{x} \in
\overline{D}_1$, then the same occurs for every superlevel set of $u$.

0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph