# Some results on minimizers and stable solutions of a variational problem

created by farina on 12 May 2011

[BibTeX]

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.