## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights

#### 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 $C(p,q)$.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 1 (2012), 1-6.

Dates
First available in Project Euclid: 30 December 2011

https://projecteuclid.org/euclid.pja/1325264388

Digital Object Identifier
doi:10.3792/pjaa.88.1

Mathematical Reviews number (MathSciNet)
MR2872207

Zentralblatt MATH identifier
1267.46051

Subjects
Primary: 35J70: Degenerate elliptic equations
Secondary: 35J60: Nonlinear elliptic equations

#### Citation

Horiuchi, Toshio; Kumlin, Peter. The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights. Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 1, 1--6. doi:10.3792/pjaa.88.1. https://projecteuclid.org/euclid.pja/1325264388

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