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.
Some remarks on the weak maximum principle / M. Rigoli, M.E. Salvatori, M. Vignati. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 21:2(2005), pp. 459-481.
Some remarks on the weak maximum principle
M. RigoliPrimo
;M.E. SalvatoriSecondo
;M. VignatiUltimo
2005
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.
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