Symmetry for positive critical points of Caffarelli-Kohn-Nirenberg inequalities

2021/05/28 by Ciraolo, Giulio, Corso, Rosario · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.13691

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 [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.

Cited by

• A Struwe-type decomposition result for weighted critical p-Laplace equations
• Sharp anisotropic L²-Caffarelli-Kohn-Nirenberg inequalities associated with the Minkowski functional

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