Heisenberg群上的Hardy不等式与Pohozaev恒等式

钮鹏程;张慧清;罗学波

数学学报 ›› 2003, Vol. 46 ›› Issue (2) : 279-290.

数学学报 ›› 2003, Vol. 46 ›› Issue (2) : 279-290. DOI: 10.12386/A2003sxxb0036
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Heisenberg群上的Hardy不等式与Pohozaev恒等式

    钮鹏程;张慧清;罗学波
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Hardy's Inequalities and Pohozaev's Identities on the Heisenberg Group

    Peng Cheng NIU,Hui Qing ZHANG,
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摘要

本文对Heisenberg群Hn上的p次Laplace算子ΔHn,p构造了基本解,建立了关于基向量场的Picone恒等式,进而建立了Hardy不等式.利用向量场的非交换运算导出了Pohozaev恒等式.这些结果均推广了Folland,Garofalo-Lanconelli已有的结果,而方法则有所改进.最后给出了在非线性次椭圆方程中的应用.

Abstract

The aim of this paper is to construct the fundamental solution of p-sub-Laplacian on the Heisenberg group and establish Hardy's inequalities by proving Pi-cone's identity on vector fields. Furthermore, Pohozaev's identities are given by using the noncommutative properties of vector fields. These results generalize those by Fol-land, Garofalo-Lanconelli, and some methods in this paper are new.

关键词

Picone恒等式 / Pohozaev恒等式 / Hardy不等式 / 基本解

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钮鹏程;张慧清;罗学波. Heisenberg群上的Hardy不等式与Pohozaev恒等式. 数学学报, 2003, 46(2): 279-290 https://doi.org/10.12386/A2003sxxb0036
Peng Cheng NIU,Hui Qing ZHANG,. Hardy's Inequalities and Pohozaev's Identities on the Heisenberg Group. Acta Mathematica Sinica, Chinese Series, 2003, 46(2): 279-290 https://doi.org/10.12386/A2003sxxb0036

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