  We consider positive critical points of Caffarelli-Kohn-Nirenberg
inequalities and prove a Liouville type result which allows us to give a
complete classification of the solutions in a certain range of parameters,
providing a symmetry result for positive solutions. The governing operator is a
weighted $p$-Laplace operator, which we consider for a general $p \in (1,d)$.
For $p=2$, the symmetry breaking region for extremals of
Caffarelli-Kohn-Nirenberg inequalities was completely characterized in [J.
Dolbeault, M. Esteban, M. Loss, Invent. Math. 44 (2016)]. Our results extend
this result to a general $p$ and are optimal in some cases.
