An Elliptic Type Gradient Estimate For the Schr\"{o}dinger Equation
Differential Geometry
2007-05-30 v1 Analysis of PDEs
Abstract
In this paper, the author discusses the elliptic type gradient estimate for the solution of the time-dependent Schr\"{o}dinger equations on noncompact manifolds. As its application, the dimension-free Harnack inequality and the Liouville type theorem for the Schr\"{o}dinger equation are proved.
Cite
@article{arxiv.0705.4178,
title = {An Elliptic Type Gradient Estimate For the Schr\"{o}dinger Equation},
author = {Qihua Ruan},
journal= {arXiv preprint arXiv:0705.4178},
year = {2007}
}