For axially symmetric domains we prove that, under suitable assumptions, there exist mountain-pass solutions which exhibit partial symmetry. Furthermore, we show that semi-stable or non-degenerate smooth solutions need to be radially symmetric in the ball.
Montoro, L., Sciunzi, B., Squassina, M., Symmetry results for the p(x)-Laplacian equation, <<ADVANCED NONLINEAR STUDIES>>, 2013; 2 (N/A): 43-64. [doi:10.1515/anona-2012-0020] [http://hdl.handle.net/10807/89017]
Symmetry results for the p(x)-Laplacian equation
Squassina, MarcoUltimo
2013
Abstract
For axially symmetric domains we prove that, under suitable assumptions, there exist mountain-pass solutions which exhibit partial symmetry. Furthermore, we show that semi-stable or non-degenerate smooth solutions need to be radially symmetric in the ball.
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