Sharp weighted-norm inequalities for functions with compact support in RN \ {0}

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Catrina, Florin²  Costa, David G.¹ 

[1] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA

[2] St Johns Univ, Dept Math & Comp Sci, Queens, NY 11439 USA

关键词: Caffarelli-Kohn-Nirenberg inequalities;    Best constants;    Positive solutions;   

DOI  :  10.1016/j.jde.2008.04.022

来源: Elsevier

【 摘 要 】

In this paper we study a class of Caffarelli-Kohn-Nirenberg inequalities without restricting the pertinent parameters. In particular, we determine the values of the corresponding optimal constants and the functions that achieve them, i.e., minimizers of a suitable functional. By studying a corresponding Euler-Lagrange equation, we also determine infinitely many sign-changing solutions at higher energy levels in addition to the found ground-state solutions. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free