数学物理学报 ›› 2004, Vol. 4 ›› Issue (6): 699-713.

• 论文 • 上一篇    下一篇

完备流形上带位势的热核估计

 王林峰   

  1. 南通师范学院数学系 南通 226007
  • 出版日期:2004-12-25 发布日期:2004-12-25
  • 基金资助:

    江苏省教育厅指导性研究课题基金资助

Estimates of Heat Kernel with Potential on Complete Manifold

 WANG Lin-Feng   

  • Online:2004-12-25 Published:2004-12-25
  • Supported by:

    江苏省教育厅指导性研究课题基金资助

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。

关键词: 位势;热方程;基本解;Harnack不等式

Abstract:

First the author  gets a gradient estimate of the heat eq uation's positive solution with potential on a complete manifold which is not compact; secondly, the author  uses the technique of geodesic to get Harnack inequ alities;moreover, the author  eatablishes two integral inequalities; together wi th Harnack inequalities, the author  gets the upper and lower bounds of heat ker nels; at last, the author  uses function's result to dominant  heat kernel of  p forms.

Key words: Potential, Heat equation, Fundamental solution, Harnack , inequality

中图分类号: 

  • 53C40