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
concentration-compactness principle
calculus
symmetry
degenerate elliptic
Author
T. Horiuchi
Ibaraki University
Peter Jan Anders Kumlin
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
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