各向异性次Laplace算子和拟p-次Laplace算子的Picone恒等式及其应用  

Picone Identities for Anisotropic Sub-Laplace Operator and Pseudo p Sub-Laplace Operator and its Applications

作　　者：冯廷福 朱艳 母贵 张克磊[2] FENG Tingfu;ZHU Yan;MU Gui;ZHANG Kelei(Department of Mathematics,Kunming University,Kunming 650214,China;Department of Mathematics and Computer Science,Guilin University of Electronic Science and Technology,Guilin 541004,China)

机构地区：[1]昆明学院数学学院,云南昆明650214 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《应用数学》2020年第2期381-392,共12页Mathematica Applicata

基　　金：国家自然科学基金青年科学基金项目(11701453,11701322);云南省教育厅科学研究基金项目(2019J0556);广西省科技厅科学研究基金项目(2017GXNSFBA198130);云南省科技厅地方高校联合专项面上项目(2019F001-078)。

摘　　要：本文首次把欧氏空间中的各向异性Laplace算子和拟p-Laplace算子分别引入到Heisenberg群Hn上,分别称为各向异性次Laplace算子和拟p-次Laplace算子,不仅建立它们相对应的Picone恒等式,而且还给出这些Picone恒等式的应用,从而把欧氏空间中的相关结果推广到Heisenberg群H^n上.In this paper,anisotropic Laplace operator and pseudo p sub-Laplace operator in the Euclidean space are introduced into Heisenberg group Hn,respectively,which are called anisotropic subLaplace operator and pseudo p sub-Laplace operator,respectively,and its corresponding Picone identities are not only established,but also the applications of these Picone identities are given,hence the results in the Euclidean space are generalized into Heisenberg group H^n.

关 键 词：HEISENBERG群 各向异性次Laplace算子 拟p-次Laplace算子 PICONE恒等式 

分 类 号：O175.2[理学—数学]