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

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).