The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights
Journal article, 2012
The main purpose of this article is to establish the CKN-type inequalities for all alpha is an element of R and to study the relating matters systematically. Roughly speaking, we shall discuss about the characterizations of the CKN-type inequalities for all alpha is an element of 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).
CKN-type inequality
Hardy-Sobolev inequality
weighted Hardy inequality
degenerate elliptic
symmetry
calculus
concentration-compactness principle
Author
T. Horiuchi
Ibaraki University
Peter Jan Anders Kumlin
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Proceedings of the Japan Academy Series A: Mathematical Sciences
0386-2194 (ISSN)
Vol. 88 1 1-6Subject Categories
Mathematical Analysis
DOI
10.3792/pjaa.88.1