带权流形上热方程的Harnack估计  

Harnack Estimate for Heat Equation on Weighted Manifolds

作　　者：阮其华[1] 陈志华[2] 

机构地区：[1]莆田学院数学系,福建莆田351100 [2]同济大学数学系,上海200092

出　　处：《数学年刊（A辑）》2008年第2期203-208,共6页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No．10571135);福建省青年基金(No．2006F3112);福建省教育厅基金(No．JA06036)资助的项目．

摘　　要：利用两种不同的方法讨论了带权流形上热方程和Schr(?)dinger方程解的Harnack估计,先利用最大模原理证明热方程解的梯度估计,从而得到解的Harnack估计,另外利用算子半群的方法证明位势函数为常数的Schr(?)dinger方程解的Harnack估计.This paper uses two different methods to prove the Harnack estimate for the solution of heat equation and Schrodinger equation on weighted manifolds. Firstly by using the maximal principle, the gradient estimate for the solution of heat equation is proved. As its application, the Harnack estimate for the solution of heat equation is obtained. On the other hand, by using the method of semigroup operator, the Harnack estimate for the solution of SchrSdinger equation with constant potential is proved.

关 键 词：带权流形 Harnack估计 热方程 

分 类 号：O186.16[理学—数学]