On the classification of extremals of Caffarelli-Kohn-Nirenberg inequalities

Giulio Ciraolo, Camilla Chiara Polvara

Published 2024-10-12Version 1

We consider a family of critical elliptic equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities, possibly in convex cones in $\mathbb{R}^d$, with $d\geq 2$. We classify positive solutions without assuming that the solution has finite energy and when the intrinsic dimension $n \in (\frac{3}{2},5]$.