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Some inequalities for the Omori-Yau maximum principle. (English) Zbl 1433.35438

Summary: 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 \(L\) 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 [A. Ratto et al., J. Funct. Anal. 134, No. 2, 486-510 (1995; Zbl 0855.58021)].

MSC:

35R01 PDEs on manifolds
35B50 Maximum principles in context of PDEs
35J15 Second-order elliptic equations
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions

Citations:

Zbl 0855.58021
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Full Text: DOI

References:

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