上半空间上的刘维尔定理
偏微分方程分析
2019-02-15 v1
摘要
本文中，我们针对上半空间上某些线性椭圆方程的下方有界解建立若干刘维尔定理。特别地，我们证明对于 ，常数是上半空间上 的边界处直至 的正解中仅有的解。
引用
@article{arxiv.1902.05187,
title = {Liouville theorems on the upper half space},
author = {Lei Wang and Meijun Zhu},
journal= {arXiv preprint arXiv:1902.05187},
year = {2019}
}
备注
Liouville Theorems for a linear equation with Dirichlet or Neuman boundary condition are obtained. Surprisedly, no boundary condition is needed for Corollary 1.3. The linear equation is closely related to our recent study of extension operators, and is closely related to Grushian type operators as well