论文标题
高阶分数laplacians的振荡现象
Oscillatory Phenomena for Higher-Order Fractional Laplacians
论文作者
论文摘要
我们收集了一些高阶分数拉普拉斯人$（-δ）^s $，$ s> 1 $的特殊性，特别注意（1,2）$ in（1,2）$的范围，这表明其振荡性质。其中包括极化和pólya-szegö的失败，以及具有签名第一个特征功能的域的明确例子。尽管存在这些波动的行为，但我们证明了Faber-Krahn的不平等仍然适用于任何$ s> 1 $的尺寸。
We collect some peculiarities of higher-order fractional Laplacians $(-Δ)^s$, $s>1$, with special attention to the range $s\in(1,2)$, which show their oscillatory nature. These include the failure of the polarization and Pólya-Szegö inequalities and the explicit example of a domain with sign-changing first eigenfunction. In spite of these fluctuating behaviours, we prove how the Faber-Krahn inequality still holds for any $s>1$ in dimension one.
