Calculus of Variations and Geometric Measure Theory
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A. Farina - E. Valdinoci

Some results on minimizers and stable solutions of a variational problem

created by farina on 12 May 2011


Accepted Paper

Inserted: 12 may 2011

Journal: Ergodic Theory and Dynamical Systems
Year: 2011


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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