[1]刘 敏,钟学秀*.一类特殊Caffarelli-Kohn-Nirenberg不等式的简单证明[J].江西师范大学学报(自然科学版),2018,(03):242-247.[doi:10.16357/j.cnki.issn1000-5862.2018.03.05]
　LIU Min,ZHONG Xuexiu*.The Simple Proof of a Special Class of Caffarelli-Kohn-Nirenberg Inequality[J].Journal of Jiangxi Normal University:Natural Science Edition,2018,(03):242-247.[doi:10.16357/j.cnki.issn1000-5862.2018.03.05]
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一类特殊Caffarelli-Kohn-Nirenberg不等式的简单证明()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2018年03期
页码:
242-247
栏目:
变分法与椭圆方程
出版日期:
2018-06-20

文章信息/Info

Title:
The Simple Proof of a Special Class of Caffarelli-Kohn-Nirenberg Inequality
文章编号:
1000-5862(2018)03-0242-06
作者:
刘 敏1; 2; 钟学秀3*
1.辽宁石油化工大学科学学院,辽宁 抚顺 113001; 2.北京师范大学数学科学学院,北京 100084; 3.中山大学数学学院,广东 广州 510275
Author(s):
LIU Min1; 2; ZHONG Xuexiu3*
1.School of Sciences,Liaoning Shihua University,Fushun Liaoning 113001,China; 2.School of Mathematical Sciences,Beijing Normal University,Beijing 100084,China; 3.Department of Mathematics,Sun Yat-sen University,Guangzhou Guangdong 510275,China
关键词:
Caffarelli-Kohn-Nirenberg不等式;  最佳常数;  Emden-Fowler变换
Keywords:
Caffarelli-Kohn-Nirenberg inequality;  best constant;  Emden-Fowler transformation
分类号:
O 177.91; O 175.29
DOI:
10.16357/j.cnki.issn1000-5862.2018.03.05
文献标志码:
A
摘要:
简单回顾一些有关Caffarelli-Kohn-Nirenberg不等式相关方面的成果,并利用Emden-Fowler变换对特殊的CKN不等式 ∫RN(|u|p)/(|x|p(1+t))dx≤(p/(N-p-pt))p∫RN(|u|p)/(|x|pt)dx,u∈C∞c(RN\{0}) 给出一个简单的证明,其中2≤p<∞,p(1+t)<N,(p/(N-p-pt))p为最佳常数.
Abstract:
Some results about the well known Caffarelli-Kohn-Nirenberg inequality are reviewed.And a simple proof of the following special CKN inequality ∫RN(|u|p)/(|x|p(1+t))dx≤(p/(N-p-pt))p∫RN(|u|p)/(|x|pt)dx,u∈C∞c(RN\{0}) is given by using the Emden-Fowler transformation,where 2≤p<∞,p(1+t)<N,and(p/(N-p-pt))p is the best constant.

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备注/Memo

备注/Memo:
收稿日期:2018-01-30
基金项目:国家自然科学基金(11701248)资助项目.
通信作者:钟学秀(1989-),女,广东徐闻人,副研究员,主要从事非线性泛函分析、变分法和偏微分方程的研究.E-mail:zhongxuexiu1989@163.com
更新日期/Last Update: 2018-06-20