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Tohoku Mathematical Journal
SECOND SERIES VOL. 66, NO. 2
|Tohoku Math. J.|
66 (2014), 259-267
A NOTE ON LOCAL GRADIENT ESTIMATE ON ALEXANDROV SPACES
Bobo Hua and Chao Xia
(Received January 22, 2013, revised June 10, 2013)
In this note, we prove Cheng-Yau type local gradient estimate for harmonic functions on Alexandrov spaces with Ricci curvature bounded below. We adopt a refined version of Moser's iteration which is based on Zhang-Zhu's Bochner type formula in . Our result improves the previous one of Zhang-Zhu  in the case of negative Ricci lower bound.
Mathematics Subject Classification.
Primary 51F99; Secondary 51K10, 53C21,31C05.
Key words and phrases.
Alexandrov spaces, harmonic functions, Yau's gradient estimate.
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