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Elliptic‐type gradient estimate for Schrödinger equations on noncompact manifolds
Author(s) -
Ruan Qihua
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm089
Subject(s) - mathematics , type (biology) , harnack's inequality , dimension (graph theory) , harnack's principle , mathematical analysis , pure mathematics , ecology , biology
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.