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

By Lucio Damascelli, Susana Merchán, Luigi Montoro, Berardino Sciunzi. 2014

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Abstract We consider weak nonnegative solutions to the critical p-Laplace equation in R N − Δ p u = u p ⁎ − 1 , in the singular case 1 p 2 . We prove that if p ⁎ ⩾ 2 then all the solutions in D 1 , p ( R N ) are radial (and radially decreasing) about some point.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/cf94a53b0caa5d2d4e39f382c5d671ec78293988