Symmetry results for the p(x)-Laplacian equation

2012/06/06 by Luigi Montoro, Montoro, Luigi, Berardino Sciunzi +3
Mathematics · #30E25 #35B07 #35J92 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:30E25 #msc:35B07 #msc:35J92 #msc:58E05

paper · pdf · doi:10.48550/arxiv.1206.1349

13 pages

arxiv created 2012/06/06 · arxiv updated 2012/06/08

Abstract

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.

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