Some Remarks on the Weak Maximum Principle

  • Marco Rigoli

    Università di Milano, Italy
  • Maura Salvatori

    Università di Milano, Italy
  • Marco Vignati

    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.

Cite this article

Marco Rigoli, Maura Salvatori, Marco Vignati, Some Remarks on the Weak Maximum Principle. Rev. Mat. Iberoam. 21 (2005), no. 2, pp. 459–481

DOI 10.4171/RMI/426