The refinement and generalization of Hardy’s inequality in Sobolev space

Journal of Inequalities and Applications

Xiaomin Xue¹  Fushan Li¹ 

[1] School of Mathematical Sciences, Qufu Normal University;

关键词: Hardy’s inequality;    Integrate by part;    Cauchy inequality;    Divergence theorem;   

DOI  :  10.1186/s13660-018-1922-5

来源: DOAJ

【 摘 要 】

Abstract In this paper, we refine the proof of Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy’s inequality from two aspects. That is to say, we extend the integral estimation function from u|x| $\frac{u}{|x|}$ to u|x|σ $\frac{u}{|x|^{\sigma }}$ with suitable σ>0 $\sigma >0$ and extend the space dimension from n≥3 $n\geq 3$ to n≥2 $n\geq 2$. Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) is the special case of our results.

【 授权许可】

Unknown