Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry and stability of non-negative solutions to degenerate elliptic
  equations in a ball   We consider non-negative distributional solutions $u\in C^1 (\bar{B_R } )$ to
the equation $-\mbox{div} [g(|\nabla u|)|\nabla u|^{-1} \nabla u ] = f(|x|,u)$
in a ball $B_R$, with $u=0$ on $\partial B_R $, where $f$ is continuous and
non-increasing in the first variable and $g\in C^1 (0,+\infty )\cap C[0,
+\infty )$, with $g(0)=0$ and $g'(t)>0$ for $t>0$. According to a result of the
first author, the solutions satisfy a certain 'local' type of symmetry. Using
this, we first prove that the solutions are radially symmetric provided that
$f$ satisfies appropriate growth conditions near its zeros. In a second part we
study the autonomous case, $f=f(u)$. The solutions of the equation are critical
points for an associated variation problem. We show under rather mild
conditions that global and local minimizers of the variational problem are
radial.

33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg