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

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.