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

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Toshio Horiuchi¹  Peter Kumlin² 

[1]Faculty of Science, Ibaraki University

[2]Department of Mathematics, Chalmers University

关键词: CKN-type inequality;    Hardy-Sobolev inequality;    weighted Hardy inequality;    degenerate elliptic equation;    best constant.;   

DOI  :  10.3792/pjaa.88.1

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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 $C(p,q)$.

【 授权许可】

Unknown