Abstract
The main purpose of this article is to establish the CKN-type inequalities for all $\alpha\in \mathbf{R}$ and to study the relating matters systematically. Roughly speaking, we shall discuss about the characterizations of the CKN-type inequalities for all $\alpha\in \mathbf{R}$ as the variational problems, the existence and nonexistence of the extremal solutions to these variational problems in proper spaces, the exact values and the assymptotic behaviors of the best constants $S(p,q,\alpha)$ and $C(p,q)$.
Citation
Toshio Horiuchi. Peter Kumlin. "The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights." Proc. Japan Acad. Ser. A Math. Sci. 88 (1) 1 - 6, January 2012. https://doi.org/10.3792/pjaa.88.1
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