Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities
- Authors: Ciraolo G.; Corso R.
- Publication year: 2022
- Type: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/529070
Abstract
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∈(1,d). For p=2, the symmetry breaking region for extremals of Caffarelli–Kohn–Nirenberg inequalities was completely characterized in Dolbeault et al. (2016). Our results extend this result to a general p and are optimal in some cases.