Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonexistence results for a class of fractional elliptic boundary value
  problems   In this paper we study a class of fractional elliptic problems of the form $$
\Ds u= f(x,u) \quad \textrm{in} \O u=0\quad \textrm{in} \R^N \setminus \O,$$
where $s\in(0,1)$. We prove nonexistence of positive solutions when $\O$ is
star-shaped and $f$ is supercritical. We also derive a nonexistence result for
subcritical $f$ in some unbounded domains. The argument relies on the method of
moving spheres applied to a reformulated problem using the Caffarelli-Silvestre
extension \cite{CSilv} of a solution of the above problem. The standard
approach in the case $s=1$ using Pohozaev type identities does not carry over
to the case $0<s<1$ due to the lack of boundary regularity of solutions.

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph