Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry of solutions to nonlocal nonlinear boundary value problems in
  radial sets   For open radial sets $\Omega\subset \mathbb{R}^N$, $N\geq 2$ we consider the
nonlinear problem \[ (P)\quad Iu=f(|x|,u) \quad\text{in $\Omega$,}\quad u\equiv
0\quad \text{on $\mathbb{R}^N\setminus \Omega$ and }\lim_{|x|\to\infty} u(x)=0,
\] where $I$ is a nonlocal operator and $f$ is a nonlinearity. Under mild
symmetry and monotonicity assumptions on $I$, $f$ and $\Omega$ we show that any
continuous bounded solution of $(P)$ is axial symmetric once it satisfies a
simple reflection inequality with respect to a hyperplane. In the special case
where $f$ does not depend on $|x|$, we show that any nonnegative nontrivial
continuous bounded solution of $(P)$ in $\mathbb{R}^N$ is radially symmetric
(up to translation) and strictly decreasing in its radial direction. Our proves
rely on different variants of maximum principles for antisymmetric
supersolutions. As an application, we prove an axial symmetry result for
minimizers of an energy functional associated to $(P)$.

34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
19
The categories of this paper are: eess