An Interpolation of Hardy Inequality and Trudinger–Moser Inequality in ℝN and Its Applications
An Interpolation of Hardy Inequality and Trudinger–Moser Inequality in ℝN and Its Applications
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DOI：
10.1093/imrn/rnp194
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发表时间：
2009-12
影响因子：
1
通讯作者：
Adimurthi;Y. Yang
中科院分区：
文献类型：
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作者：
Adimurthi;Y. Yang
我们在rn （N≥2）中建立了Hardy不等式和Trudinger-Moser不等式的插值。表示u u 1,τ≤1 1 RNτ= R N(|∇u | 1 | x | eβαu N +τ| | | | u N) dx N / N (N−1)−2−m = 0 1 / N对任何τ> 0。这里有α m|u|mN/(N−1)m！dx 0。
We establish an interpolation of Hardy inequality and Trudinger–Moser inequality in R N (N ≥ 2). Denote u u 1,τ ≤1 1,τ RN = R N (|∇u| 1 |x|β eα|u| N+ τ |u| N )dx N/(N−1)N−2−m=0 1/N for any τ > 0. There holds α m|u|mN/(N−1) m!dx 0.