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

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 Rd, with d≥2. We classify positive solutions without assuming that the solution has finite energy and when the intrinsic dimension n∈(52,5].