Symmetry breaking of extremals for the Caffarelli-Kohn-Nirenberg inequalities in a non-Hilbertian setting

Abstract

We provide an explicit necessary condition to have that no extremal for the best constant in the Caffarelli-Kohn-Nirenberg inequality is radially symmetric.

11 pages

References in corpus (2)

• Weighted Sobolev spaces of radially symmetric functions
• Symmetry of extremals of functional inequalities via spectral estimates for linear operators

Cited by in corpus (2)

• Sharp pointwise estimates for weighted critical $p$-Laplace equations
• A tool for symmetry breaking and multiplicity in some nonlocal problems