一类积分不等式及其变分计算  

Integral Inequalities and Their Calculus of Variations

作　　者：王贝[1] 雷雨田[2] 

机构地区：[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

出　　处：《吉林大学学报（理学版）》2012年第5期957-960,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10871097)

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Lp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.Hardy-Littlewood-Sobolev （HLS） inequality and the Wolff inequality were used to obtain the Lp estimate of the Wolff potentials. At the same time, Euler-Lagrange equations of the extremal functions for the more general weighted HIS inequalities were also established by means of the method of calculus of variations.

关 键 词：Hardy-Littlewood-Sobolev不等式 Wolff位势 变分计算 分数阶微分方程组 

分 类 号：O175.5[理学—数学]