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| 摘要: |
Engel群是次黎曼几何中的一类重要的单连通幂零李群.本文研究了Engel群E=(R4,o,{δλ})的有界区域Ω上次Laplace算子ΔE的狄利克雷特征值问题{(-ΔE)3u-λu, in Ω,
u=∂u/∂v=∂2u/∂v2=0, on ∂Ω其中v是边界∂Ω的单位外法向量场.我们建立了该问题的一些万有特征值不等式. |
| 关键词: 特征值 不等式 Engel群 次拉普拉斯算子 |
| DOI： |
| 分类号:O175.9;O186.1 |
| 基金项目: |
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| INEQUALITIES FOR EIGENVALUES OF THE SUB-LAPLCAIN ON THE ENGEL GROUP |
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BAI Chen,SUN He-jun
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| Abstract: |
| The Engel groups are one important kind of simply connected nilpotent Lie groups in sub-Riemannian geometry. In this paper, we investigate the Dirichlet eigenvalue problem of the sub-Laplacian ΔE on a bounded domain Ω of the Engel group E=(R4,o,{δλ}) as follows {(-ΔE)3u-λu, in Ω, u=∂u/∂v=∂2u/∂v2=0, on ∂Ω, where v is the outwards unit normal vector field of ∂Ω. We establish some universal inequalities for eigenvalues of this problem. |
| Key words: eigenvalue inequality Engel group sub-Laplacian |
