【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.更多还原

【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.更多还原