论文标题
与二阶Sobolev嵌入相关的非线性方程的特征值和特征值
The eigenvalues and eigenfunctions of the non-linear equation associated to second order Sobolev embeddings
论文作者
论文摘要
我们考虑将$ l^p $表征到$ l^q $ sobolev二阶嵌入的非线性特征值方程，用于线段两端的Navier边界条件。我们对S-numbers的完整说明和一般情况下的极端功能$（p，q）\ in（1，\ infty）^2 $。除其他结果外，我们还表明，当且仅当$ \ frac {1} {p} {p}+\ frac {1} {q} = 1 $时，可以用相关一阶嵌入的嵌入方式表示这些。我们的发现为Banach空间设置中高级Sobolev空间的惊人性质提供了新的启示。
We consider the non-linear eigenvalue equations characterizing $L^p$ into $L^q$ Sobolev embeddings of second order for Navier boundary conditions at both ends of a line segment. We give a complete description of the s-numbers and the extremal functions in the general case $(p,q)\in(1,\infty)^2$. Among other results, we show that these can be expressed in terms of those of related first order embeddings, if and only if $\frac{1}{p}+\frac{1}{q}=1$. Our findings shed new light on the surprising nature of higher order Sobolev spaces in the Banach space setting.
