Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities. (March 2022)

• Record Type: Journal Article
• Authors: Ciraolo, Giulio; Corso, Rosario
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: 35J92 -- 35B53 -- 35B09 -- 53C21; Caffarelli–Kohn–Nirenberg inequalities -- Optimal constant -- Classification of solutions -- Quasilinear anisotropic elliptic equations -- Liouville-type theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112683
• Languages: English
• ISSNs: 0362-546X

Abstract

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.