Engle群上次Laplace算子的特征值不等式  

INEQUALITIES FOR EIGENVALUES OF THE SUB-LAPLCAIN ON THE ENGEL GROUP

作　　者：白晨[1] 孙和军[1] ZHANG Xue-ying;WANG Chao-yue;ZHANG Chuan-zhou;XIAO Jun(College of Science,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]南京理工大学数学与统计学院,江苏南京210094

出　　处：《数学杂志》2023年第5期409-421,共13页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China (11001130);Fundamental Research Finds for the Central Universities (30917011335)。

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=(R^(4),■,{δλ})的有界区域Ω上次Laplace算子△_(E)的狄利克雷特征值问题■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.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 Δ_(E) on a bounded domain Ω of the Engel group E=(R^(4),■,{δλ}) as follows■ where v is the outwards unit normal vector field of ?Ω.We establish some universal inequalities for eigenvalues of this problem.

关 键 词：特征值 不等式 Engel群 次拉普拉斯算子 

分 类 号：O175.9[理学—数学] O186.1[理学—基础数学]