Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local analysis of solutions of fractional semi-linear elliptic equations
  with isolated singularities   In this paper, we study the local behaviors of nonnegative local solutions of
fractional order semi-linear equations $(-\Delta)^\sigma
u=u^{\frac{n+2\sigma}{n-2\sigma}}$ with an isolated singularity, where
$\sigma\in (0,1)$. We prove that all the solutions are asymptotically radially
symmetric. When $\sigma =1$, these have been proved in \cite{CGS} by
Caffarelli, Gidas and Spruck.

30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn