| 一类Heisenberg群上的非线性方程的解之弱可微性 |
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| 引用本文： | 杨孝平,赵培标. 一类Heisenberg群上的非线性方程的解之弱可微性[J]. 南京理工大学学报(自然科学版), 2003, 27(5): 647-652 |
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| 作者姓名： | 杨孝平 赵培标 |
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| 作者单位： | 南京理工大学理学院,南京,210094;南京理工大学理学院,南京,210094 |
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| 基金项目： | 国家自然科学基金 (197710 4 8) |
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| 摘 要： | 该文利用分数阶差商和先验估计，证明一类Heisenberg群上的非线性次椭圆方程的W2,2-弱可微性。这类问题是欧氏空间上的偏微分方程在一般度量空间上的发展，在几何控制与数学物理中有着非常重要的应用。
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| 关 键 词： | 次椭圆 Heisenberg群 弱可微性 |
| 修稿时间： | 2003-03-11 |
Weak Differentiability of Solutions for Nonlinear Sub-elliptic Equations in the Heisenberg Group |
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| YangXiaoping ZhaoPeibiao. Weak Differentiability of Solutions for Nonlinear Sub-elliptic Equations in the Heisenberg Group[J]. Journal of Nanjing University of Science and Technology(Nature Science), 2003, 27(5): 647-652 |
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| Authors: | YangXiaoping ZhaoPeibiao |
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| Abstract: | With the help of fractional difference quotients, the W 2,2 -weak differentiability of solutions for a nonlinear sub-elliptic equation in the Heisenberg group is established. This is a generalization of theory for partial differential equations in Euclidean spaces to that of general metric spaces. There are many important applications in geometrical control theory and mathematical physics. |
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| Keywords: | sub-elliptics Heisenberg group weak differentiability |
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