We consider the functional integral vertical bar del u vertical bar(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 <= 3 and in any dimension for non-zero rotation vectors.
Farina, A., Valdinoci, E. (2012). Some results on minimizers and stable solutions of a variational problem. ERGODIC THEORY & DYNAMICAL SYSTEMS, 32, 1302-1312 [10.1017/S0143385711000198].
Some results on minimizers and stable solutions of a variational problem
VALDINOCI, ENRICO
2012-01-01
Abstract
We consider the functional integral vertical bar del u vertical bar(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 <= 3 and in any dimension for non-zero rotation vectors.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
