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| ON THE UPPER ESTIMATES OF FUNDAMENTAL SOLUTIONS OFPARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS |
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Citation： |
Li Jiayu,Shao Xin.ON THE UPPER ESTIMATES OF FUNDAMENTAL SOLUTIONS OFPARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS[J].Chinese Annals of Mathematics B,1995,16(1):119~130 |
| Page view： 1024
Net amount： 718 |
Authors： |
Li Jiayu; Shao Xin |
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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 $t$. |
Keywords： |
Parabolic equation, Gradient estimate, Harnack
inequality, Fundamental solution, Riemannian manifolds. |
Classification： |
58G35 |
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