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Gradient Estimates and a Liouville Type Theorem for the Schrödinger Operator

✍ Scribed by E.R. Negrin

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
164 KB
Volume
127
Category
Article
ISSN
0022-1236

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✦ Synopsis

In this paper, we derive a Liouville type theorem on a complete Riemannian manifold without boundary and with nonnegative Ricci curvature for the equation (\Delta u(x)+h(x) u(x)=0), where the conditions (\lim _{r \rightarrow x} r^{-1} \cdot \sup {x \in B{p}(r)}|\nabla h(x)|=0) and (h \geqslant 0) imposed by P. Li and S.-T. Yau (Acta Math. 156 (1986), 153-201) and Jiayu Li (J. Funct. Anal. 100 (1991), 233-256), respectively, are replaced by a weaker condition than both of them, namely, (\lim _{r} \ldots r^{-2} \cdot \inf {x \in B{p}(r)} h(x)=0). Cl 1995 Academic Press, Inc.

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