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Abstract and Applied Analysis
Volume 2015, Article ID 410896, 7 pages
http://dx.doi.org/10.1155/2015/410896
Research Article

Some Inequalities for the Omori-Yau Maximum Principle

Korea Institute for Advanced Study, Hoegiro 85, Seoul 130-722, Republic of Korea

Received 22 January 2015; Revised 25 June 2015; Accepted 2 July 2015

Academic Editor: Leszek Gasinski

Copyright © 2015 Kyusik Hong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We generalize A. Borbély’s condition for the conclusion of the Omori-Yau maximum principle for the Laplace operator on a complete Riemannian manifold to a second-order linear semielliptic operator with bounded coefficients and no zeroth order term. Also, we consider a new sufficient condition for the existence of a tamed exhaustion function. From these results, we may remark that the existence of a tamed exhaustion function is more general than the hypotheses in the version of the Omori-Yau maximum principle that was given by A. Ratto, M. Rigoli, and A. G. Setti.