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arXiv:1206.1349 [math.AP]AbstractReferencesReviewsResources

Symmetry results for the $p(x)$-Laplacian equation

Luigi Montoro, Berardino Sciunzi, Marco Squassina

Published 2012-06-06Version 1

We consider the Dirichlet problem for the nonlinear $p(x)$-Laplacian equation. 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.

Comments: 13 pages
Categories: math.AP
Subjects: 30E25, 35B07, 58E05, 35J92
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