Radial symmetry and applications for a problem involving the \(-\Delta_p(\cdot)\) operator and critical nonlinearity in \(\mathbb{R}^N\) (Q406300)

The present papers deals with weak nonnegative solutions to the critical \(p\)-Laplace equation NEWLINE\[NEWLINE-\Delta_p u=u^{p^*-1}\text{ in }\mathbb{R}^N,NEWLINE\]NEWLINE where \(1<p<2\leq N\), \(p^*:=\frac{N_p}{N-p}\geq 2\). Using the Moving Plane Method and Sobolev's inequality, the authors prove that all the solutions in a certain class are radial and radially decreasing with respect to some point.