On the Caffarelli-Kohn-Nirenberg-type inequalities involving critical and supercritical weights

摘要

The main purpose of this article is to establish the Caffarelli-Kohn-Nirenberg-type (CKN-type) inequalities for all α∈R and to study the related matters systematically. Roughly speaking, we discuss the characterizations of the CKN-type inequalities for all α ∈ R as the variational problems, the existence and nonexistence of the extremal solutions to these variational problems in proper spaces, and the exact values and the asymptotic behaviors of the best constants in both the noncritical case and the critical case.