We consider the functional (formula presente) 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 3 and in any dimension for non-zero rotation vectors.
Some results on minimizers and stable solutions of a variational problem / A. Farina, E. Valdinoci. - In: ERGODIC THEORY & DYNAMICAL SYSTEMS. - ISSN 0143-3857. - 32:4(2012), pp. 1302-1312.
Some results on minimizers and stable solutions of a variational problem
E. Valdinoci
2012
Abstract
We consider the functional (formula presente) 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 3 and in any dimension for non-zero rotation vectors.
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