| Heisenberg群上的Hardy不等式与Pohozaev恒等式 |
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| 引用本文： | 钮鹏程,张慧清,罗学波.Heisenberg群上的Hardy不等式与Pohozaev恒等式[J].数学学报,2003,46(2):279-290. |
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| 作者姓名： | 钮鹏程 张慧清 罗学波 |
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| 作者单位： | 西北工业大学应用数学系,西安,710072 |
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| 基金项目： | 国家自然科学基金资助项目(19971068) |
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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.
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| 关 键 词： | 基本解 Hardy不等式 Picone恒等式 Pohozaev恒等式 |
| 文章编号： | 0583-1431(2003)02-0279-12 |
| 修稿时间： | 2001年2月13日 |
Hardy's Inequalities and Pohozaev's Identities on the Heisenberg Group |
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| Peng Cheng NIU Hui Qing ZHANG Xue Bo LUO.Hardy''''s Inequalities and Pohozaev''''s Identities on the Heisenberg Group[J].Acta Mathematica Sinica,2003,46(2):279-290. |
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| Authors: | Peng Cheng NIU Hui Qing ZHANG Xue Bo LUO |
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| Institution: | Peng Cheng NIU Hui Qing ZHANG Xue Bo LUO(Department of Applied Mathematics, Northwestern Polytechnical University,Xi'an 710072, P. R. China) (Fax: (029)8491000; E-mail: lzh@iped.xjtu.edu.cn) |
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| 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. |
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| Keywords: | Fundamental solution Hardy's inequality Picone's identity Pohozaev's identity |
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