具有加权测度的H型群上漂移Laplace算子的Levitin-Parnovski型特征值不等式  

LEVITIN-PARNOVSKI-TYPE INEQUALITY FOR EIGENVALUES OF THE DRIFTING LAPLACIAN ON THE H-TYPE GROUP WITH THE WEIGHTED MEASURE

作　　者：韩承月 孙和军[1] 江绪永 HAN Cheng-yue;SUN He-jun;JIANG Xu-yong(College of Science,Nanjing University of Science and Technology,Nanjing 210014,China)

机构地区：[1]南京理工大学理学院,江苏南京210014

出　　处：《数学杂志》2018年第5期861-868,共8页Journal of Mathematics

基　　金：国家自然科学基金资助(11001130);中央高校基本科研业务费专项基金资助(30917011335)

摘　　要：本文研究了具有加权测度dμ=e^(-φ)dv的H型群G上漂移Laplace算子-?_G+<▽_Gφ,▽_G(·)>的Dirichlet特征值问题,建立了该问题的Levitin-Parnovski型特征值不等式,推广包含了Ilias和Makhoul对Heisenberg群上次Laplace算子所获得的结果 (J. Geom. Anal.,2012, 22(1):206–222).In this paper,we study the Dirichlet eigenvalue problem of the drifting Laplacian-△G+(▽G,▽G(.))on the H-type group G with the weighted measured d1=e?'dv.We establish a Levitin-Parnovski universal inequality for eigenvalues of this problem,which generalize the result derived by Ilias and Makhoul for the Kohn Laplacian on the Heisenberg group(J.Geom.Anal.,2012,22(1):206-222).

关 键 词：H型群 特征值 漂移Laplace算子 

分 类 号：O175.9[理学—数学] O186.1[理学—基础数学]