| ON THE UPPER ESTIMATES OF FUNDAMENTAL SOLUTIONS OF PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS |
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| 作者姓名： | Li Jiayu Shao Xin |
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| 作者单位： | Departmellt of Mathematics，Anhui University，Hefei 230039，China.Basic Department，Anhui Agricultural College，Hefei 230036，China. |
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| 摘 要： | ＯＮＴＨＥＵＰＰＥＲＥＳＴＩＭＡＴＥＳＯＦＦＵＮＤＡＭＥＮＴＡＬＳＯＬＵＴＩＯＮＳＯＦＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳＯＮＲＩＥＭＡＮＮＩＡＮＭＡＮＩＦＯＬＤＳ￥ＬＩＪＩＡＹＵ；ＳＨＡＯＸＩＮ（ＤｅｐａｒｔｍｅｌｌｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ａ...
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| 关 键 词： | 抛物型方程 偏微分 斜度估算 基础解 黎曼流形 |
| 收稿时间： | 1992/6/30 0:00:00 |
| 修稿时间： | 1992/10/26 0:00:00 |
ON THE UPPER ESTIMATES OF FUNDAMENTAL SOLUTIONS OF
PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS |
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| Li Jiayu,Shao Xin.ON THE UPPER ESTIMATES OF FUNDAMENTAL SOLUTIONS OF
PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS[J].Chinese Annals of Mathematics,Series B,1995,16(1):119-130. |
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| Authors: | Li Jiayu and Shao Xin |
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| Institution: | DepartmentofMathematics,AnhuiUniversity,Hefei230039,China. |
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| Abstract: | The authors first derive gradient estimates and Harnack inequalities for
positive solutions of the equation
$$ \De u(x,t) + b(x,t) \cdot \nabla u(x,t) + h(x,t) u(x,t) - \f{\pa
u(x,t)}{\pa t} = 0 $$
on complete Riemannian manifolds, and then derive upper bounds of any
positive $L^2$ fundamental solution of the equation when $h(x,t)$ and
$b(x,t)$ are independent of $t$. |
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| Keywords: | Parabolic equation Gradient estimate Harnack inequality Fundamentalsolution Riemannian manifolds |
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