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数学进展 - 2016, Vol. 45(6): 932-938
研究论文
Carnot群上双调和函数的均值定理
A Mean Value Theorem for Bi-harmonic Function on Carnot Group

谭沈阳1,黄体仁2, 张学华3
TAN Shenyang1, HUANG Tiren2, ZHANG Xuehua3

1. 南京理工大学泰州科技学院基础部, 泰州, 江苏, 225300;
2. 浙江理工大学数学系, 杭州, 浙江, 310018;
3. 黄山学院数理统计学院, 黄山, 安徽, 245041
1. Taizhou Institute of Sci. $\&$ Tech., NUST, Taizhou, Jiangsu, 225300, P. R. China;
2. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, 310018, P. R. China;
3. Department of Mathematics and Statistics, Huangshan, Anhui, 245041, P. R. China

收稿日期: 2014-12-17
出版日期: 2016-11-10
2016, Vol. 45(6): 932-938
DOI: 10.11845/sxjz.2014210b


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摘要 本文通过迭代方法得到了Carnot群上双调和函数的均值定理, 同时利用该均值定理得到了Carnot群上双调和算子的全局Liouville定理.
Abstract:This paper mainly gets a mean value theorem for bi-harmonic function by iteration method on Carnot group. As an application of this theorem, a global Liouville theorem about the bi-harmonic operator on Carnot group is proved.
PACS:  O175.25  
基金资助:国家青年自然科学基金(No. 11401531)和江苏省高校自然科学基金(No. 14KJD110004).
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