Heisenberg群上p-次Laplace算子的Dirichlet特征值估计

Dirichlet eigenvalue estimates for p-sub-Laplacian in the Heisenberg group

我们研究了Heisenberg群Hn中具有光滑边界的域上p-次Laplace算子的Dirichlet特征值问题.运用Ljusternik-Schnirelman原理,我们给出了特征值序列的存在性,然后利用有界域上的Hardy型不等式,给出了基本特征值率的估计.

We study the Dirichlet eigenvalue problem for the p-Laplace operator on a bounded domain in the Heisenberg group H^n. Using the Ljusternik-Schnireman principle, we show the existence of a sequence of eigenvalues. Then we give the estimate of the fundamental eigenvalue ratio, using the Hardy-type inequality on the bounded do-main.