Symmetry results for critical $p$-Laplace equations

It is known that positive solutions to $\Delta_p u + u^{p^*-1}=0$ in $\mathbb{R}^n$, with $n \geq 3$ and $1
We provide a new approach to this problem which allows us to give a complete classification of the solutions in an anisotropic setting as well as to a suitable generalization of the problem in convex cones.

This is a joint work with A. Figalli and A. Roncoroni.