An Elliptic Type Gradient Estimate For the Schrödinger Equation

Details An Elliptic Type Gradient Estimate For the Schrödinger Equation An Elliptic Type Gradient Estimate For the Schrödinger Equation

2007-05-29

arxiv.org/abs/0705.4178v1

Mathematics

Differential Geometry

Scientific paper

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.

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