Revista Matemática Iberoamericana


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Volume 21, Issue 2, 2005, pp. 459–481
DOI: 10.4171/RMI/426

Published online: 2005-08-31

Some Remarks on the Weak Maximum Principle

Marco Rigoli[1], Maura Salvatori[2] and Marco Vignati[3]

(1) Università di Milano, Italy
(2) Università di Milano, Italy
(3) Università di Milano, Italy

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.

Keywords: Maximum principles, volume growth

Rigoli Marco, Salvatori Maura, Vignati Marco: Some Remarks on the Weak Maximum Principle. Rev. Mat. Iberoam. 21 (2005), 459-481. doi: 10.4171/RMI/426