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Some remarks on the weak maximum principle.

Marco RigoliMaura SalvatoriMarco Vignati — 2005

Revista Matemática Iberoamericana

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.

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