| 完备流形上带位势的热核估计 |
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| 引用本文： | 王林峰. 完备流形上带位势的热核估计[J]. 数学物理学报(A辑), 2004, 4(6): 699-713 |
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| 作者姓名： | 王林峰 |
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| 作者单位： | 南通师范学院数学系 南通226007 |
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| 基金项目： | 江苏省教育厅指导性研究课题基金资助 |
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| 摘 要： | 在完备非紧流形上获得了关于带位势热方程正解的梯度估计；接着，利用测地线的技巧获得了Harnack不等式；进一步，建立了两个积分不等式，综合Harnack不等式获得了热核的上下界；最后，利用函数的结果来控制p形式的热核。
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| 关 键 词： | 位势 热方程 基本解 Harnack不等式 |
| 文章编号： | 1003-3998(2004)06-699-15 |
| 修稿时间： | 2002-04-30 |
Estimates of Heat Kernel with Potential on Complete Manifold |
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| WANG Lin-Feng. Estimates of Heat Kernel with Potential on Complete Manifold[J]. Acta Mathematica Scientia, 2004, 4(6): 699-713 |
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| Authors: | WANG Lin-Feng |
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| Abstract: | First the author gets a gradient estimate of the heat equation's positive solution with potential on a complete manifold which is not compact; secondly, the author uses the technique of geodesic to get Harnack inequalities;moreover, the author eatablishes two integral inequalities; together with Harnack inequalities, the author gets the upper and lower bounds of heat kernels; at last, the author uses function's result to dominant heat kernel of %p% forms. |
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| Keywords: | Potential Heat equation Fundamental solution Harnack inequality. |
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