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.
Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities / G. Ciraolo, R. Corso. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 216(2022), pp. 112683.1-112683.23. [10.1016/j.na.2021.112683]
Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities
G. Ciraolo;
2022
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.File | Dimensione | Formato | |
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