Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry results for stable and monotone solutions to fibered systems of
  PDEs   We study the symmetry properties for solutions of elliptic systems of the
type {ll}-\dive(a_1(x,|\nabla u^1|(X))\nabla u^1(X))=F_{1}(x, u^1(X),...,
u^n(X)), ... -\dive(a_n(x,|\nabla u^n|(X))\nabla u^n(X))=F_{n}(x, u^1(X),...,
u^n(X)), where $x\in \R^m$ with $1\leq m< N$, $X=(x,y)\in \R^m\times \R^{N-m}$,
and $F_{1},..., F_{n}$ are the derivatives with respect to $\xi^1,..., \xi^n$
of some $F=F(x,\xi^1,..., \xi^n)$ such that for any $i=1,..., n$ and any fixed
$(x,\xi^1,..., \xi^{i-1},\xi^{i+1},..., \xi^n)\in \R^m\times \R^{n-1}$ the map
$\xi^i\to F(x,\xi^1,...,\xi^i,..., \xi^n)$ belongs to $C^2(\R)$. We obtain a
Poincar\'e-type formula for the solutions of the system and we use it to prove
a symmetry result both for stable and for monotone solutions.

14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th