| 非紧流形上抛物方程的椭圆型梯度估计 |
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| 引用本文： | 吴佳贤,黄琴.非紧流形上抛物方程的椭圆型梯度估计[J].漳州师院学报,2010(4):6-12. |
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| 作者姓名： | 吴佳贤 黄琴 |
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| 作者单位： | [1]漳州师范学院数学与信息科学系,福建漳州363000 [2]莆田学院数学系,福建莆田351100 |
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| 基金项目： | 福建省教育厅A类科技项目（JA09202; JA08193） |
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| 摘 要： | 给出完备非紧黎曼流形M上的抛物方程ut=△u＋Xu＋hu的正解的全局梯度估计,该估计与M的维数n无关.这里X是任意非零C 1向量场;h是定义在M×（0,＋∞）上的非负函数,对于自变量x是C 1函数.作为应用,我们将给出该方程的解的Harnack估计.
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| 关 键 词： | 完备非紧流形 抛物方程 梯度估计 Harnack估计 Laplacian比较定理 |
Elliptic-Type Gradient Estimate for a Parabolic Equation on Noncompact Manifolds |
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| WU Jia-xian,HUANG Qin.Elliptic-Type Gradient Estimate for a Parabolic Equation on Noncompact Manifolds[J].Journal of ZhangZhou Teachers College(Philosophy & Social Sciences),2010(4):6-12. |
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| Authors: | WU Jia-xian HUANG Qin |
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| Institution: | 1.Department of Mathematics and Information Science,Zhangzhou Normal University,Zhangzhou,Fujian 363000,China;2.Department of Math,Putian University,Putian,Fujian 351100,China) |
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| Abstract: | In this paper,we study a global gradient estimate for the positive solution to the following parabolic equation on a complete noncompact Riemannian manifold,where X is an any nonzero vector field,and h is a negative function defined on which is in the x-variable.As an application,the dimension-free Harnack estimate for the above parabolic equation（1.2） is proved. |
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| Keywords: | complete noncompact manifold parabolic equation gradient estimate Harnack estimate Laplacian comparison theorem |
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