论文标题
对准椭圆系统的第一个特征值的比较估计值
Comparison estimates on the first eigenvalue of a quasilinear elliptic system
论文作者
论文摘要
我们研究了完全紧凑的riemannian歧管上的差异性特征值问题的系统。特别是，回收了$（p，q）$ - laplacian的第一个特征值的Faber-Krahn比较估计和不平等。最后，我们谴责了$ p $ -laplacian的Cheeger类型估算值，$ 1 <p <\ infty $，从cheeger的第一个特征值（P，Q）$ -Laplacian的第一个特征值来看，从Cheeger的持续估算值来看。作为推论，第一个特征值将Cheeger的常数收敛为$ p，q \ to 1,1。$。
We study a system of quasilinear eigenvalue problems with Dirichlet boundary conditions on complete compact Riemannian manifolds. In particular, Cheng comparison estimates and inequality of Faber-Krahn for the first eigenvalue of a $(p,q)$-Laplacian are recovered. Lastly, we reprove a Cheeger type estimates for $p$-Laplacian, $1<p<\infty$, from where a lower bound estimate in terms of Cheeger's constant for the first eigenvalue of a $(p,q)$-Laplacian is built. As a corollary, the first eigenvalue converges to Cheeger's constant as $p,q\to 1,1.$
