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arXiv · 1406.6162

Radial symmetry and applications for a problem involving the $-\Delta_p(\cdot)$ operator and critical nonlinearity in~$\mathbb{R}^N$

Lucio Damascelli·Susana Merchan·Luigi Montoro·Berardino Sciunzi
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Abstract

We consider weak non-negative solutions to the critical $p$-Laplace equation in $\mathbb{R}^N$, $-\Delta_p u =u^{p^*-1}$ in the singular case $1<p<2$. We prove that if the nonlinearity is locally Lipschitz continuous, namely $p^*\geqslant2$ then all the solutions in ${\mathcal D}^{1,p}(\R^N)$ are radial (and radially decreasing) about some point.

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Lucio Damascelli, Susana Merchan, Luigi Montoro, Berardino Sciunzi. 2014-06-24. Radial symmetry and applications for a problem involving the $-\Delta_p(\cdot)$ operator and critical nonlinearity in~$\mathbb{R}^N$. https://arxiv.org/abs/1406.6162

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