论文标题
径向对称函数的两个关键Rellich不平等的显式最佳常数
Explicit optimal constants of two critical Rellich inequalities for radially symmetric functions
论文作者
论文摘要
我们考虑了两个关键的Rellich不平等现象，在较高的临界径向radial sobolev spaces $ w_ {0，{\ rm rad}}}^{k，p} $中，在原点和边界上都具有奇异性，其中$ 1 <p = \ frac {n} {n} {k} $。我们给出了$ w_ {0，{\ rm rad}}}^{k，\ frac {n} {k}}} $中的两个关键雷利希不等式的最佳常数的显式值。此外，还讨论了最佳常数的（不可实现）。
We consider two critical Rellich inequalities with singularities at both the origin and the boundary in the higher order critical radial Sobolev spaces $W_{0, {\rm rad}}^{k, p}$, where $1< p = \frac{N}{k}$. We give the explicit values of the optimal constants of two critical Rellich inequalities for radially symmetric functions in $W_{0, {\rm rad}}^{k, \frac{N}{k}}$. Furthermore the (non-)attainability of the optimal constants are also discussed.
