6533b82dfe1ef96bd1290bc2
RESEARCH PRODUCT
Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities
Giulio CiraoloRosario Corsosubject
Pure mathematicsApplied MathematicsOperator (physics)Caffarelli–Kohn–Nirenberg inequalities Classification of solutions Liouville-type theorem Optimal constant Quasilinear anisotropic elliptic equationsMathematics::Analysis of PDEsType (model theory)Range (mathematics)Settore MAT/05 - Analisi MatematicaSymmetry breakingSymmetry (geometry)Nirenberg and Matthaei experimentLaplace operatorAnalysisMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-03-01 |