Hardy Inequalities In The Certain Domains

In this article, I studied a type of Hardy's inequality. The Hardy inequality is a classical result in mathematical analysis, in which the best constant is usually related to geometry. From then on, many mathematicians extended the Hardy's inequality to more general situations.Let Ω(?)Rn (n≥1) be a bounded domain in Rn, and Bρ={x||x|≤ρ} a subset in Ω. Based on the work of Filippas, Moschini, Tertikas, Farit Avkhadiev and Ari Laptev, I proved the following result:For (?)u∈H01(Ω\Bρ), in which:This theorem extends some Hardy type inequalities before. I have also considered some other cases.