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January 2012 The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights
Toshio Horiuchi, Peter Kumlin
Proc. Japan Acad. Ser. A Math. Sci. 88(1): 1-6 (January 2012). DOI: 10.3792/pjaa.88.1

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 $C(p,q)$.

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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

Information

Published: January 2012
First available in Project Euclid: 30 December 2011

zbMATH: 1267.46051
MathSciNet: MR2872207
Digital Object Identifier: 10.3792/pjaa.88.1

Subjects:
Primary: 35J70
Secondary: 35J60

Rights: Copyright © 2012 The Japan Academy

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Vol.88 • No. 1 • January 2012
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