Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A maximum principle on unbounded domains and a Liouville theorem for
  fractional p-harmonic functions   In this paper, we establish the following Liouville theorem for fractional
\emph{p}-harmonic functions.
  {\em Assume that $u$ is a bounded solution of $$(-\lap)^s_p u(x) = 0, \;\; x
\in \mathbb{R}^n,$$ with $0<s<1$ and $p \geq 2$.
  Then $u$ must be constant.}
  A new idea is employed to prove this result, which is completely different
from the previous ones in deriving Liouville theorems.
  For any given hyper-plane in $\mathbb{R}^n$, we show that $u$ is symmetric
about the plane. To this end, we established a {\em maximum principle} for
anti-symmetric functions on any half space. We believe that this {\em maximum
principle}, as well as the ideas in the proof, will become useful tools in
studying a variety of problems involving nonlinear non-local operators.

8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th