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Bulletin of the London Mathematical Society Advance Access originally published online on December 22, 2007
Bulletin of the London Mathematical Society 2007 39(6):982-988; doi:10.1112/blms/bdm089
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© 2007 London Mathematical Society

Elliptic-type gradient estimate for Schrödinger equations on noncompact manifolds

Qihua Ruan

School of Mathematics
Zhongshan University
Guangzhou
Guangdong, 510275
P. R. China
ruanqh@sysu.edu.cn

Received 21 July 2006. Revision received 18 May 2007.

In this paper, the author discusses an elliptic-type gradient estimate for the solution of the time-dependent Schrödinger equations on noncompact manifolds. As an application, the dimension-free Harnack inequality and a Liouville-type theorem for the Schrödinger equation are proved.

Current address: Department of Mathematics Putian University Putian Fujian, 351100 P. R. China

Project partially supported by the Young Scholar Fund of Fujian Province, No.2006F3112, and the Department of Education of Fujian Province, Fund No. JA06036.

2000 Mathematics Subject Classification 58G11 (primary), 53C21 (secondary).


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