Accepted Paper
Inserted: 12 may 2011
Journal: Ergodic Theory and Dynamical Systems
Year: 2011
Abstract:
We consider the functional
$$ \int \frac{
\nabla u
2}{2}+F(x,u)\,dx$$
in a periodic setting.
We discuss whether the minimizers or the stable solutions
satisfy some symmetry or monotonicity properties,
with special emphasis on the autonomous case
when $F$ is $x$-independent.
In particular, we give an answer to a question posed by Victor Bangert when $F$ is autonomous in dimension $n\le3$ and in any dimension for nonzero rotation vectors.
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