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arXiv · 1206.1349

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

Luigi Montoro·Berardino Sciunzi·Marco Squassina
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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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Luigi Montoro, Berardino Sciunzi, Marco Squassina. 2012-06-06. Symmetry results for the $p(x)$-Laplacian equation. https://arxiv.org/abs/1206.1349

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