Revista Matemática Iberoamericana

Some Remarks on the Weak Maximum Principle

Marco Rigoli, Maura Salvatori, and Marco Vignati

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Abstract

We obtain a maximum principle at infinity for solutions of a class of nonlinear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumptions of volume growth conditions. In the case of the Laplace-Beltrami operator we relate our results to stochastic completeness and parabolicity of the manifold.

Article information

Source
Rev. Mat. Iberoamericana, Volume 21, Number 2 (2005), 459-481.

Dates
First available in Project Euclid: 11 August 2005

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1123766803

Mathematical Reviews number (MathSciNet)
MR2174913

Zentralblatt MATH identifier
1110.58022

Subjects
Primary: 58J05: Elliptic equations on manifolds, general theory [See also 35-XX] 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Keywords
maximum principles volume growth

Citation

Rigoli, Marco; Salvatori, Maura; Vignati, Marco. Some Remarks on the Weak Maximum Principle. Rev. Mat. Iberoamericana 21 (2005), no. 2, 459--481. https://projecteuclid.org/euclid.rmi/1123766803


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