一类积分不等式及其变分计算

J4 ›› 2012, Vol. 50 ›› Issue (05): 957-960.

一类积分不等式及其变分计算

王贝¹, 雷雨田²

1. 江苏教育学院数学系, 南京 210013|2. 南京师范大学数学科学学院, 南京 210046

收稿日期:2011-09-19 出版日期:2012-09-26 发布日期:2012-09-29
通讯作者: 王贝 E-mail:jsjywang@126.com

Integral Inequalities and Their Calculus of Variations

WANG Bei¹, LEI Yutian²

1. Department of Mathematics, Jiangsu Institute of Education, Nanjing 210013, China;2. School of Mathematics Science, Nanjing Normal University, Nanjing 210046, China

Received:2011-09-19 Online:2012-09-26 Published:2012-09-29
Contact: WANG Bei E-mail:jsjywang@126.com

摘要/Abstract

摘要：

利用HardyLittlewoodSobolev不等式和Wolff型积分不等式得到了Wolff型位势的L^p估计, 并利用变分方法得到了较加权的HLS型更一般的不等式最佳函数满足的EulerLagrange方程.

关键词: HardyLittlewoodSobolev不等式, Wolff位势, 变分计算; 分数阶微分方程组

Abstract:

HardyLittlewoodSobolev (HLS) inequality and the Wolff inequality were used to obtain the L^p estimate of the Wolff potentials. At the same time, EulerLagrange equations of the extremal functions for the more general weighted HLS inequalities were also established by means of the method of calculus of variations.

Key words: HardyLittlewoodSobolev inequality, Wolff potential, calculus of variations, fractional order partial differential equations (PDEs)

中图分类号:

O175.5

王贝, 雷雨田. 一类积分不等式及其变分计算[J]. J4, 2012, 50(05): 957-960.

WANG Bei, LEI Yu-Tian. Integral Inequalities and Their Calculus of Variations[J]. J4, 2012, 50(05): 957-960.